You’re definitely using different muscles.

The elliptical is closer to swimming than running. Consider:
you are not really fighting gravity
you have normalized resistance on your legs AND arms
you are performing a low impact exercise
your form and technique plays a much larger role in your efficiency than muscular endurance

Running:

needs the ability to adapt to varying terrain and muscular demands change minute to minute.
needs you to work against gravity and maintain forward momentum
requires a completely different technique

You may also be starting out too fast.
Don’t give up.

You might be in good shape, but running is something you have to get used to. It is uncomfortable compared to an elliptical, and will feel that way until you get used to it. The more you run, the better you will become over time the more you get used to the rigors of running.