Parsing is almost always a part of a programming language compiler but it doesn't have to be.

When we parse a string, we go up from low-level human-readable strings to intermediate parse trees to a high-level AST.

A process of compilation goes down from some kind of a high-level internal representation through phases to something that is close to the target low-level language.

It can go down from an AST, or LLVM-s internal representation, or whatever.

Problems solved by both processes are different:

1. Parsing is about finding string patterns (using regexps or PEGs or whatever) and representing these using a more strict high-level structure. The structure is usually tree-like but is also often a graph.

2. Compiling takes something high-level (a tree, a graph, etc) and emits something different, usually simplified.

A good example is a typical lisp implementation where the parser is trivial but compilation phases represent numerous simplifying phases.

The amount of time being consumed by parsing is vanishingly small. It's a lot like the decoding time spent on x86 code is marginal nowadays compared to the speculative and reordering logic.

YACC was called "Yet Another Compiler Compiler" because back in the day parsing was the bulk of compilation, now it's relatively minimal.