Or is there an alternative tool (perhaps some option to isearch?) that would show just the matches in a separate buffer linked to the original buffer?

Use-case

I have a log file with very long lines. When the matching line appears in *occur* buffer, it is still too cluttered to be useful (due to wrapping and a lot of extra info).

It isn't difficult to write something like this, but it seems so basic that it must've been done before.

If my explanation wasn't good enough, think about grep -Po search-string.