Is there anything like Layer-2 MTU and layer-3 MTU? if yes, then what is the purpose of two different MTUs and how are they related?

Yes, There is L-2 MTU and L-3 MTU.

It depends on the size of Interfaces and technology which used.

Be clear in the place of L3 MTU it is basically IP MTU.

for general purpose, L2 MTU is Ethernet frame MTU which is larger in size since additional L-2 frame header is added.