Hullo and welcome!
Sadly, no simple statements. This subject of how to bring up poly with potential new squeezes has been discussed a lot just because there is no one catch word to sum it all up. Do a tag search on 'dating' and see what others have come up with.
As to the specific question of whether to describe the philosophy or the practice I would take the practice, and if further questions arise, make sure to mention 'polyamory', 'responsible non-monogamy', 'non-exclusiveness' or whatever you think describes your situation best. If they are interested, they will check out Google or Wikipedia, or ask you outright.
The biggest confusion I see people having is confusing responsible non-monogamy with cheating. Something quite casual like 'my boyfriend has been going on dates with this girl, and I think she's really cute and they seem to be getting on fine' or whatever circumvents the problem some people have with blurting out 'I'm polyamorous' or 'You need to know I have a live-in bf', since it doesn't always ring a bell and would imply that you are actually thinking this new thing is going to be a relationship. Cheating and seeking out affairs is something that makes culturally a lot more sense, as it were, so that is what people will automatically assume in most cases.
As to general aversion to labels - you need to establish a certain level of common language with anyone you meet in order to be mutually understood. It doesn't have to be polyamorous or boyfriend or a even a relationship, but something that even if it doesn't 100 % describe your life philosophy communicates something across the board. I lean towards 'ATM I'm dating someone but we are not exclusive', but there are really lots of ways people have chosen to tell the same thing. Read around a bit and see what feels right to you.
Me: bi female in my twenties