A (grammatical) marker is a °clitic or an °affix.
Linguists almost never discuss the meaning of "(grammatical) marker", but the term is very widely used, especially in the description of non-European languages, where it is taken as a cover term for an affix and a function word (= clitic). Matthews's (2007) definition (as the "realization of a unit") is too vague, and also too broad because one would say, for example, that plural can be "realized" as vowel change, but vowel change would not be considered as a marker.