Is 700x38c bicycle tire the same as a 26 bicycle tire?

700C means 622 mm, 26" can mean anything from 559 to 599 mm, with the latter being quite rare. The wheels might fit, but if it's a rim braked bike there's no way the old brakes are going to reach the new rims. Current MTBs (which are 26"/559 mm) can usually take 700C wheels with narrow tires. But you need them to be either disc braked or to use an adapter plate to get rim brakes to work. 700C(622 mm) in a frame meant for 27"(630 mm) often work out just fine, but you might have to switch to something called long-reach brakes though. 27" was an old road standard, so that's a fairly common swap.