Apply to both.

I did that this past winter. I interviewed for both. The position I was most qualified for had been tentatively filled but the person backed out after accepting the offer. So they offered it to me. It was the higher paying position.

If it's a large consulting firm, I'd apply to both. Unlikely that they would even track that you applied to two positions unless they were with the same team, which seems unlikely.

OP here. if they think I’m not qualified for the stretch, do you think theres a good chance they’ll refer me to the lower level opening?

I'd apply for the one I feel is better for me at that time in my career. If they were equal-level positions in different departments or handling different tasks, I'd say go for it, but since they are different levels, I would definitely only go for one.

I am currently job hunting. I'd like to an apply at a large consulting firm and I see two positions I could be a fit for. One is a project/program management level (level I currently work at), and another is a director/VP level. In this situation would you apply to both? Or the stretch position?