What is the difference between a merger and a consolidation?

If you're talking about qualified plans, I'm not sure there is any distinction. If there is one, I think the only distinction is that if you merge plan a into plan b you end up with one plan, plan b; whereas, if you consolidate plan a with plan b, you end up with one new plan, plan c (with a new ERISA plan number and a new plan effective date). Even then, however, I don't think there is any other distinction from a Code or ERISA perspective.