Are the words "apparatus" and "equipment" synonyms?
Within a lab they are synonymous. But if you consider in general, apparatus refer to non-machines. Equipment on the other hand can be divided into a couple of sections:


Non-mechanical which can be things like kitchen equipment, measuring cups, knives (all hand tools)   
Mechanical machines which are things like sewing machines, mechanical diggers.   
Powered machines that are powered by either gas, steam or electricity.