An adposition is a °flag that is not an °affix.
That adpositions and case affixes are functionally similar has long been recognized, but it was only after Haspelmath (2005) that the general term "flag" (which was coined in the 1980s) gained ground. Flags are defined as a kind of bound morphs, and the difference between case affixes and adpositions is simply that the former are affixes while the latter are not affixes.
Since bound morphs that are not affixes (or roots) are clitics, one can also say that adpositions are clitic flags. Note that the definition excludes forms that are called "adpositions" but are actually adverbs because they can occur on their, as free forms (e.g. English before).
adposition (STR) = a flag which occurs as an independent word, in contrast to a case affix. Adpositions are distinguished by position: preposition, postposition, and circumposition. (Section 4.3)
"Adpositions ... may be defined as grammatical tools which mark the relationship between two parts of a sentence: one is the element which an adposition governs. It is traditionally called its complement and is mostly represented by a noun or noun-like word or phrase. It will be called here the governed term. The other part is an entity which either functions as the predicate of this sentence, or is a non-predicative noun. Adpositions mark, therefore, the fact that, from the syntactic point of view, their governed term depends on a head." (Hagège 2010: 1)