Often when people are seeing each other in an unofficial capacity, communication is not high on the list of priorities. It's a bit difficult to ask 'What are we doing?" or "What do you want out of this/ Where is this going?", when there has been no formal request for exclusivity or mention of 'love' etc. It's a grey area, as it were. Breaking up is never easy, it's always uncomfortable and difficult, even painful. But sometimes it is inevitable and necessary.
You can be a coward and just stop answering their calls, hoping they get the message and move on. It's a pretty spineless, uncaring way to go, but it's a choice. You can do a slow-ghosting, not much better than the first option, but certainly a little kinder. In this instance, you just slowly phase the person out, becoming more 'busy', and not returning calls here and there, until communication winds down.
Assuming the unofficial connection is agreed upon and acceptable to both parties, then a polite text or call to say you've met someone and can't see this person any longer, could suffice. It's also pretty spineless and cowardly, the easy way out. But for a casual 'thing', it can be acceptable in this day and age. And perhaps the kindest option, the talk. Bring her/ him to coffee or dinner, tell them you need to talk, and explain that while your time with them has been enjoyable/ special/ whatever, you need to move on/ you've met someone/ you need some time alone/ whatever your excuse :)
Hopefully you can still be friends, but never lead someone on, and never take responsibility for their needs or feelings. Be polite and caring, but if they flip out (another reason to be in a public place!), just respond with "I'm sorry you feel that way." And "I sincerely wish you the best. Bye."
The mature, direct approach is always best - regardless of what transpires, they'll always respect you for being brave enough to address it up front, and for having the integrity to approach them face to face, as opposed to taking the coward's way out. A man builds his reputation and record every day, in everything he does. What do you want on your record...? ;)