"Consulting" is a term so generic and ill-defined it almost doesn't mean anything at all.

When I did software consulting, I was basically a decent "modern" web dev brought into crusty old companies to bring some new perspective and approach. I'd help with some project direction and initial implementation and try to get a team up to speed to continue the work. I typically embedded as part of the team for a while and did plenty of hands-on design, coding, and troubleshooting work right alongside.

But this was just a small consulting shop, not one of the big "strategic" consultancies. Very different worlds.