The responses you've got so far aren't wrong, but there's an easier way to think about this:
Connectionless: Drop a postcard in the mail and stop thinking about it. Maybe it gets there, maybe not.
Connection-oriented: Start a correspondence. If you don't get a response after a while, send your letter again. If you get parts 1, 2, and 4 you say "Hey, I missed #3, send that again please!" You keep thinking about the flow of conversation whether you have a message in hand right now or not.
The "connection" is in your memory. On a computer, that may involve persistent memory use on network hardware, by your OS kernel, and in the program sending the messages while the connection exists.
Connectionless: Drop a postcard in the mail and stop thinking about it. Maybe it gets there, maybe not.
Connection-oriented: Start a correspondence. If you don't get a response after a while, send your letter again. If you get parts 1, 2, and 4 you say "Hey, I missed #3, send that again please!" You keep thinking about the flow of conversation whether you have a message in hand right now or not.
The "connection" is in your memory. On a computer, that may involve persistent memory use on network hardware, by your OS kernel, and in the program sending the messages while the connection exists.