What do you call the 12-24 hour aspect of a timestamp? (not format)

I will go out on a limb and say there isn't one: it's 24-hour format or 12-hour format.

Generally, English is an efficient language in that it re-uses words; it doesn't define more words than it needs. Thus English would describe the format, it doesn't have a word for the format until the description becomes so cumbersome or used so often that a shorter way of expressing it is needed.

Thus we don't have a word for a hard-back book (even the single word hard-back or hardback is really an adjective with book being omitted as understood). We don't have a word for brilliant white paint as opposed to white or off-white. Even a queue is often qualified as a queue of people. We don't have a word for roof-tile as opposed to wall-tile.

An exception which proves the rule might be telephone: that word has been associated with desk-bound phone apparatus for so long that mobile phone (that is, an adjective qualifying phone) was needed, and now the concept is so ubiquitous that simply mobile suffices.

Some of these specific examples don't hold for American English (which has line for queue and cell for mobile) but the general principle does. It's simply how the language works.

Timestamp usually consist of Date, Time and Timezone(like UTC, IST). Eventhough the term is coined as timestamp, this isn't something which is completely related to time alone.

so,

you can better term timestamp format to refer different timestamp formats and

you can term time formats to refer 24hr format and 12hr format