This is a very good question.
Generally speaking, the smaller the number is, the longer that acciaccatura should sustain. An 8th acciaccatura could theoretically be played as long as an 8th note, an so forth. Given in the same piece, at the same tempo, an 8th acciaccatura could sound longer and clearer, and thus more defined or more emphasized than those 16th, and 32th.
If you are trying to play those notations on piano, it's not a good idea to take those 8th, 16th, 32th acciaccatura....too pedanticly. The purpose of an acciaccatura is usually bringing out certain accent of the music. How that accent exactly should sound, is largely interpretable. Some pianists use their gut feelings some like to play that based on research of the style of that piece or even the personality and biography of the composer. I would suggest you listen to good recordings of that piece for samples of the interpretation. Knowledge of the style, the music history and the composer may also help.
More tricky than acciaccature are things like tremolo. Baroque works for harpsichord have lots of those stuff. How to play it? It's rather a matter of taste than technique. Education builds good taste. I would recommend the master classes taught by Sir András Schiff (you can find them on YouTube). Pick any of his master classes, and learn by heart. He doesn't necessarily teach you how to play an acciaccatura or tremolo, but he has very good taste, he teaches music.
I myself play another instrument (a kind of lute), but refer to Schiff's teaching when I play music.
FYI, the traditional repertoire of my instrument involves a huge amount of embellishment such as tremolo, acciaccatura, portamento, and on and on. Until I came across your question, I never really paid close attention to the notations. I just follow my teacher's demo, learn music style and history, refer to Schiff's master classes, and sometimes use imagination.
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The author clarified his question like this:
I'm asking from the perspective of the composer. That's why it so
important. If I had to play somebody's music and saw such notes, I
probably wouldn't pay much attention to it.
If, in the same piece, a composer uses both 8th and 16th for the acciaccatura, then he may suggest there should be some difference between these two. Like I explained above, if he wants to emphasize an acciaccatura more than another, he could note that more defined one with 8th, the less dominant one with 16th. In my repertoire, many pieces have a group of pitches as an acciaccatura, it would be wise to use 16th or 32th for each pitch in the group, otherwise, this acciaccature would appear way too dominant, it would no longer be an embellishment, rather the main note. This should not happen.
If, that piece has only a few acciaccatura, and those acciaccatura are not grouped, then there's hardly any difference of using 8th or 16th or 32th. It's a quick crush, an embellishment, an accent. That's it.