This is a distinction that ceased being meaningful 10ish years ago. Even the big management consulting firms run a combination of staff aug and strategy advice on most projects because there are so many more dollars for staff aug and project work than there are for advice.

Yes, there are advice-only consultants and clients looking for that, but "consulting" is a bucket of work that encompasses a lot of different things. Trying to force a distinction is kind of elitist and not really in line with reality.

Source: been consulting for the last 12 years with firms of several sizes and focuses.