I completely agree with what
@Kola has said here. I think that's a phenomenal explanation.
While PE houses often engage in M&A work, I think it's slightly back-to-front to say abstractly that PE = M&A. I would really encourage you to see them as separate and distinct: PE work has so many nuances and requires real specialists that not every M&A lawyer could manage a deal for a PE house.
The other thing to remember (on a more basic level) is that M&A does stand for Mergers and Acquisitions. In my mind, that's a bit of a misnomer for most PE work which is almost invariably focussed on partial or full-stake acquisitions.
In any case, I dont want to wildly overcomplicate things, so would reiterate Kola's point to consider PE an industry focus which will use specialist transactional-focussed teams.