Hi Juan,
There is an important difference between the two.
A host looks at a destination IP address and decides whether the destination is inside or outside its own subnet. When it’s outside its own subnet, it does an ARP request for the default gateway, gets a reply from the default gateway, then sends the IP packet to the default gateway.
With proxy ARP, a host thinks that the destination is in its own subnet while in reality, it’s not…it’s on another subnet. The host does an ARP request for the destination and the default gateway responds “on behalf” of the device on the other subnet.
On a LAN, proxy ARP works but it’s basically a misconfiguration issue where you have an incorrect subnet mask on a host.
Hope this helps!
Rene