Both plants like similar mesic conditions and so can be found in similar locations. However, these plants are actually very easy to tell apart using only a few easily observable characteristics*.
Bark:
* _Ostrya_ is peely/shreddy brown
* _Carpinus_ is smooth and grey. The bark almost looks sinewy, leading to its much better common name: muscle wood.
Leaves are both doubly serrate and similar in size. However, leaf texture is different:
* _Ostrya_ is finely hairy. Best to feel with lips (more sensitive) when 1st getting used to difference.
* _Carpinus_ is smooth (glabrous) and even somewhat papery like _Fagus_.
* now, if I could only remember which one had the _hop_ in its name! (this is why I stick to scientific names :p)
I'll update with sources soon.