If the box with your c3 in it had a filter that was shorter than the c3p.. someone swapped filters.
The c3 and c3p are virtually identical in size.. though as you noticed.. the c3 is about 4$ & has no gasket, whereas the c3p is about 8$ and has a gasket. Also.. the c3-p has lots more filter media in it... And looks better constructed. I.e., it has a filter paper over cover.. etc..
If I were doing an oil change on a machine that was going to need another oil change quick..like one that had been setting, and had lots of MMO in the oil helpin ghte valves and rings seat.. or if I was doing the first oil change after a blown head gasket.. etc. I would use the cheaper one.. as it was only going to be a 'few hour filter'
For the filter that I ran for 50 or 100 hours.. I would go with more media.