Indo-European spatial prepositions, when analyzed across all attested languages, are rich in beautiful, unexpected relationships.
You could think that the spatial relationships (above, below, beside, etc.) are independent of the language studied, but that is not so. Like everything in language, the world is first articulated, in a language specific way, into concepts (e.g., spatial relationships worth naming) and then each concept is articulated again into a sequence of meaningless sounds that form the word to stand for that concept (e.g., a spatial preposition).
When you try to translate those prepositions into another language, you often end up with lots of synonymy and homonymy, but that is largely only apparent - because the concepts do not match. What appears to be blatant synonymy on one side of a translation may involve very little semantic overlap in the other language. The confusing effect is caused by assuming certain arbitrary context during the translation and then contradicting that by assuming that the translation covers the entire lexical unit in all possible contexts. With grammatical words such as prepositions, translation word-for-word doesn't tend to work. They are very much language dependent and context dependent, even more than nouns or verbs.
Latin "ad" can be a translation, in certain contexts, of any of English "at", "on", "toward, "among", "against" (plus of various temporal and other relationships as well). This is entirely unsurprising. There is not a 1-1 mapping between spatial concepts in English and spatial concepts in Latin.
I did not list "above" nor "up", though. If you focus on "assumptio" = "taking up", this occurrence of "up" is not a spatial one at all. As such it does not approach the possible spatial meanings of "super" ("above", "over", "beyond") at all.
So while apparent synonymy between spatial prepositions, especially if freely moving back and forth between two languages is extremely common to find, this question is not an example of one.