The reason Blue Beech (Musclewood) and Ironwood (Hop Hornbeam) both get called "Ironwood" is mainly because of their extremely dense, tough wood. However, they are actually quite different trees. Here's how they compare:

Why Are Both Called "Ironwood"?
Hard, strong wood: Both species have some of the hardest wood found in North America. Early settlers and woodworkers named them "ironwood" because they were so difficult to cut or work with.
Regional naming differences: In Canada and the U.S., the name "Ironwood" is often used for Ostrya virginiana. However, in some areas, Carpinus caroliniana is also called "Ironwood" because of its toughness.

Distinct appearances: Despite both being called Ironwood, they look very different. Please see chart. 

In Summary
If you're in moist, lowland forests, it's probably Blue-Beech (Musclewood) (Carpinus caroliniana).
If you're in dry, well-drained upland forests, it's likely Ironwood (Hop-Hornbeam) (Ostrya virginiana).
Both are called Ironwood, but Ostrya virginiana is more commonly recognized by that name.