bitcoind is the command-line software for Bitcoin Core. It stands for "Bitcoin Daemon" where a daemon is any computer process which runs in the background ("service" in Windows terminology).
bitcoind is the name of the command line software for Bitcoin Core. It does exactly the same things as Bitcoin Core except that it has no GUI interface. To interact with bitcoind, you must use the bitcoin-cli tool or another tool that can communicate over its Remote Procedure Call (RPC) interface (e.g. curl). bitcoind's RPC interface adheres to the JSON-RPC 1.0 specification.
bitcoind uses the same source code as Bitcoin Core for all of its functionality. The only code differences are those involved in the GUI; that code is not needed for bitcoind. bitcoind is a full node wallet software. It will verify every single block and transaction that it receives and relay the valid ones. As a wallet software it also handles private keys and sending and receiving Bitcoin.
