With UDP sockets, the server receves packets, and the client sends them

ow! That's not true. For starters, UDP doesn't know anything of client and server. sundialsvc4 has a great answer you should read.

Both the server and the client can both send and receive. Both the client and server almost always both send and receive. (Conversations are generally variations of the following: The client sends a request, the server receives a request, the server sends a response, the client receives a response.)