The Bitcoin P2P network
The Bitcoin P2P network is a randomly-wired gossip network. This means that all nodes make arbitrary connections to other peers (using various ways to discover new addresses) using a custom TCP protocol, usually using port 8333. Typical nodes create 8 outgoing connections, and if publicly reachable, accept up to a few 100 incoming connections.
It being a gossip network means that nodes send messages to each other of the form "do you have block with hash X" or "do you have transaction with hash X", after which the peer can respond by asking for the full transaction or block. Simplified, this means that eventually every node learns about every block. The protocol is bidirectional - it doesn't matter who connected to whom; both peers will announce if they have something they don't know the other side already has as well.
Not all network nodes are reachable. Some only make outgoing connections. Sometimes setups are used where someone runs a publicly reachable node, and then runs a second private node that only connects out to their own public node, thereby giving some extra privacy and reduced attack surface.
Not all network nodes validate the blocks and transactions they see and pass on. Nodes that do are called full nodes.
Miners (or at least mining pools) run nodes like this, picking up transactions their nodes learn about, assembling them into candidate blocks, hashing to find a nonce, and if they succeed, broadcast the resulting block out to their peers using the same P2P network. Miners in this way are not special - people don't directly submit things to miners.
Since recently, an extension to the protocol is used to relay blocks much more efficiently, called Compact Blocks. It makes use of the fact that most nodes will already have most of the transactions that are added to a new block.
Specialized relay networks
Additional networks exist of groups of nodes that use specialized protocols to very quickly interconnect nodes. One such protocol is FIBRE, which is in fact UDP based and makes heavy use of error correcting codes to avoid roundtrips.
Ironically, Electrum in your question is a bad example. Electrum is not a P2P client (not even a light one). Intead, it uses a client-server architecture, and connects to specialized servers (which are themselves Bitcoin P2P nodes however).