How is parsing a word of a formal language wrt its formal grammar defined?

In computer science and linguistics, parsing, or, more formally, syntactic analysis, is the process of analyzing a text, made of a sequence of tokens (for example, words), to determine its grammatical structure with respect to a given (more or less) formal grammar.

Is there a formal definition, or a more clear one, for parsing a word of a formal language wrt its formal grammar defined? I am not able to understand the meaning of parsing, because I am stuck at the term "grammatical structure" of a word wrt the formal grammar.

2. About analytic grammar and parsing from Wikipedia:

Though there is a tremendous body of literature on parsing algorithms, most of these algorithms assume that the language to be parsed is initially described by means of a generative formal grammar, and that the goal is to transform this generative grammar into a working parser. Strictly speaking, a generative grammar does not in any way correspond to the algorithm used to parse a language, and various algorithms have different restrictions on the form of production rules that are considered well-formed.

An alternative approach is to formalize the language in terms of an analytic grammar in the first place, which more directly corresponds to the structure and semantics of a parser for the language.

What do "generative grammar" and "analytic grammar" mean?

Isn't that true that formal grammars are always "generative" in the sense that they generate formal languages?

Thanks and regards!

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