NETWORK_ID is a 16 byte identifier that allows Monero nodes to identify themselves to other nodes, in order to prevent different Monero networks (e.g. mainnet vs stagenet) from accidentally talking to each other. It has nothing directly to do with wallet addresses, although there are different wallet address prefixes designed for use on different networks.
The web site you've linked to uses the the separate term "Network Byte", and shows the hex representations of what src/cryptonote_config.h defines using decimal numbers instead.
E.g. a network byte of 0x12 in hex is the number 18 in decimal, which is why the web site you've linked defaults to the value 12 and the cryptonote_config.h defines the value as
CRYPTONOTE_PUBLIC_ADDRESS_BASE58_PREFIX = 18;