On this trip or during the trip?

Hey
Recently, Ive been confused about the uses of and the difference between ON and DURING.

I heard both, and they seem to be interchangeable in sentences like "Some of the members lost their wallet ON/DURING the trip,"
but my question here is, what's the exact difference in meaning between them?

I know for sure that when you say "They lost their wallet DURING the trip" it simply means WHILE ON (engaged in) the trip, they lost their treasured possession, but I dont quite get it when you say "They lost their wallet ON the trip." Does this mean the members lost the wallet which was on the trip or the members who were on the trip lost their wallet?

Same thing with other activity/state-related words like "vacation" or "holiday." I heard people say "What did you do ON your holiday?", but this kinda throws me off because in my mind, I'm thinking the sentences should be changed to "What did you do (while on/during) your holiday?"
Hell, even in the song "Holiday" by Green Day, Billie Joe Armstrong says, "This is our lives on holiday." Is he saying that his live is on holiday or that is his life WHILE he's on holiday? It just seems kind of ambiguous...which is on holiday? Him or his life?

Hmm I realized that I kind of strayed from my original question. If the ON in "Some members lost their wallet on the trip" does mean "Some members lost their wallet while they were on the trip," does the only difference in meaning between DURING and ON lie in the fact that DURING is more closely related to time whereas ON is more closely related to the active engagement in a particular activity?

Any thoughts would be greatly appreciated!