Patients can't really tell most of the time because they aren't dentists. Like the above answers, a crown covers the entire tooth all the way around and the veneer just covers the front of the tooth. Hold a mirror inside your mouth in front of another mirror and see if you see your own tooth color or a porcelain color of a particular tooth. But really? Just ask your DDS.
Why not try asking your dentist? It would not hurt to say you are confused and would like to know the difference between the two and why he used one over the other.
Veeners cover the front and tips of the tooth where the crown literally wraps around the entire tooth. You can see if it is a veneer from the back of your tooth. Your dentist should have explained to you his treatment plan and made sure you were ok with it. I am sorry you were not given enough information.
