I'm curious. Which type of ability is understanding a weekly pill tray?

She is losing ALL of her skills.
Every single one of these skills, surprisingly, goes into loading a pill tray.
We have little idea how much our brains have to work to coordinate something that those of us with function do so automatically, and believe to be so easy.
I can tell you that, at about 75 or 80, you will notice differences in your OWN brain. You will be less adaptable. You won't be able to multitask anymore (drive and text? Out of the question. Check our groceries and listen to hubby tell you about needing gas? Nope, you won't hear him). You will be flummoxed and wonder how you ever were able to do three things at once.

You might want to do a lot of online explorations about dementia, how it effects the brain. A good place to start with your questions regarding filling a pill tray is to look up "List of EXECUTIVE functions". This will give you a list of about ten things that a brain must be able to do to do one single thing.

I would also ask you to watch anything you can find online such as Teepa Snow and her films, about the mind with dementia.
My brother and I could sit and endlessly discuss how his mind, beset by early Lewy's Dementia, reacted to and saw the world as opposed to how mine did.
He once said to me "I am not glad to know what I have, and where it will take me if I have to live longer, but I AM glad to know why I see the world so differently now".

It is said that we lose our executive functioning gradually over the years at such a slow rate that we/others don't recognize it. FINALLY it is noticed that we aren't paying our bills. To pay our bills we must RECOGNIZE a bill has come (separate it from other meaningless mail), must REMEMBER how we pay bills, must ORGANIZE where we keep a checkbook and REMEMBER how to use checks, keep records. We must be able to coordinate a whole raft of things to get a single check in the mail for a single payment.

I would say the King of functions is memory. The Queen may be organization. We have to know, for instance, "I take pills. I have to take pills because............. I take pills at a certain hour. Some pills I take in the morning because.............. Some pills at night because. This pill helps me with this. That with that" and so on.
Then we have to be able to organize things so we remember. So "I have a box to organize them. I have to remember how to organize." And on you go.

Look up brain "neurons".
Look up brain "synapses" and see all the little tentacles that have to connect to do any single simple thing. Look up "parasympathetic system" and "sympathetic system".

There's more to learning about the brain than we could do in one lifetime.
If you looked up the urinary system and how it works in the brain you would have a month's long work to make out the complications involved, but you sure would understand incontinence better.

In the end, caring for a senior, we need to learn enough to know only how to protect them, and how to have empathy for a condition we cannot ever fully understand even with a solid 7 yearsof medical study.

So glad you have a curious mind.
The internet is going to be your best friend!

BlueHeron, after reading your profile, I think your Mom should move into Memory Care, not Assisted Living. With Memory Care, the Staff is familiar with all aspects of dementia.

My Dad was also having problems remembering to take his medicine when he was living in a Independent Living facility, so I opted for the "Med Tech" who took over control of Dad's medicine and would bring to him, twice a day, whatever meds were needed at that time. Yes, there was a fee for this service which was added onto Dad's rent. A few months later, the facility recommended Dad move to their Memory Care section.

You ask the question but you are doing the right thing for her. Just wait as things get worse and she can no longer walk or swallow. Most of us are in it or have taken the same caregiver journey. She has lost cognitive function, telling time and is no longer safe. If the fire alarm went off, she might not know what that means

I just chalked any changes in my Mom up to the disease. I did not try to analyze it. Nothing u can do about it. Just be thankful that in the AL they are incharge of her medication. She will be given the right pill at the right time on the right day.

This is called executive ability. And the really goofy thing is that she might lose some executive function, might only lose it periodically, or might lose it then get it back, or might never lose it. My mom can dress herself perfectly when I pick out the clothes and lay them out all together, but if I show her a single piece of clothing by itself (like just a bra or just a shirt), she has no idea how to put it on, let alone what it is called. Dementia is the most evil disease!

One day to the next is the same to her - Happens with years too . Concept of time , Dates , Months , Years .

"Does understanding a calendar relate to other functions?"

You bet it does!

What DAY is today?
Can she answer correctly?
(Orientated to day)

If you ask again on 20mins will she know? (Short term memory)

If told it is Wednesday, can she connect Wednesday in the correct order to the other days of the week? Eg name what yesterday was? What tomorrow will be?
(Processing)

What pills do I take tomorrow from a pre-marked month pack?
(Planning)

Losing calender skills, losing *time* can happen in many ways.

*Executive Functioning* would be a broad label. The above is juts my guessess! I wish I knew more specfic medical labels to offer you. (Homework for me)

Executive function.
IADL.
She can not formulate a plan , understand, follow or execute a plan of action .

Frontal Lobes Functions:

Attention 
Concentration
Self-Monitoring
Organization
Expressive Language (Speaking)
Motor Planning & Initiation
Awareness of Abilities
Awareness of Limitations
Personality
Mental Flexibility
Inhibition of Behavior
Emotions
Problem Solving
Planning
Judgment
An injury to the frontal lobes may affect an individual’s ability to control emotions, impulses, and behavior or may cause difficulty recalling events or speaking.


Temporal Lobes Functions:

Memory
Understanding Language (Receptive Language)
Sequencing
Hearing
Organization

Source: https://www.biausa.org/brain-injury/about-brain-injury/what-is-a-brain-injury/function-of-the-brain

"What is frontotemporal dementia?

Frontotemporal dementia (FTD), a common cause of dementia, is a group of disorders that occur when nerve cells in the frontal and temporal lobes of the brain are lost. This causes the lobes to shrink. FTD can affect behavior, personality, language, and movement.

The cause of FTD is unknown. Researchers have linked certain subtypes of FTD to mutations on several genes. Some people with FTD have tiny structures, called Pick bodies, in their brain cells. Pick bodies contain an abnormal amount or type of protein.

A family history of FTD is the only known risk for these diseases. Although experts believe that some cases of FTD are inherited, most people with FTD have no family history of it or other types of dementia.

Symptoms of FTD start gradually and progress steadily, and in some cases, rapidly. They vary from person to person, depending on the areas of the brain involved.

These are common symptoms:

Behavior and/or dramatic personality changes, such as swearing, stealing, increased interest in sex, or a deterioration in personal hygiene habits
Socially inappropriate, impulsive, or repetitive behaviors
Impaired judgment
Apathy
Lack of empathy
Decreased self awareness
Loss of interest in normal daily activities
Emotional withdrawal from others
Loss of energy and motivation
Inability to use or understand language; this may include difficulty naming objects, expressing words, or understanding the meanings of words
Hesitation when speaking
Less frequent speech
Distractibility
Trouble planning and organizing
Frequent mood changes
Agitation
Increasing dependence

Some people have physical symptoms, such as tremors, muscle spasms or weakness, rigidity, poor coordination and/or balance, or difficulty swallowing. Psychiatric symptoms, such as hallucinations or delusions, also may occur, although these are not as common as behavioral and language changes."

Source: https://www.hopkinsmedicine.org/health/conditions-and-diseases/dementia/frontotemporal-dementia#:~:text=What%20is%20frontotemporal%20dementia%3F,personality%2C%20language%2C%20and%20movement.

Honestly it sounds like your mom should be in Memory Care not ALF.
The fact that she can "read" the words does not mean she understands them.
I can "read" words in Spanish, French, German but I sure don't know what they mean or understand them.