are these parts the same?

No they aren't the same, but very similar.

I wouldn't say one has more processor than the other.
i3-6100 is slightly older than the 7th Generation Pentiums, they offer similar performance. And the Pentium should have a few slight advantages on certain specific tasks.
 
No they're not the same.

The first one is the Intel Core i3-6100. It was released a little while back (6th generation of Intel CPUs or "Skylake"). It has 2 cores with hyper-threading (i.e., making it 4 threads). Its base clock speed is 3.70GHz.

The second on is the Intel Pentium G4560. It was just recently released (7th generation of Intel CPUs or "Kaby Lake"). Like the Core i3, it also has 2 cores with hyper-threading (4 threads). But its base clock speed is at 3.50GHz.

Both can be plugged in motherboards with LGA1151 sockets (for example, Skylake motherboards B150, H110 and H170; and Kaby Lake motherboards B250 and H270). Note that you *MIGHT*/*WILL* need to update BIOS if you are to use a different generation CPU with a different generation motherboard having the same socket.