The “P” in “P bass” doesn’t stand for Percussion, but for Precision. If you’re learning the lingo, you might as well learn it correctly 
The most important difference between J and P basses is the tone, due to the different pickup configuration already mentioned. One other difference that might be important is the neck shape. J basses tend to have narrower necks, which are usually easier to play. Something you might want to consider as well. Of course, there’s also the option of getting a P/J bass, which has one split-coil pickup closer to the neck (like a P bass) and one single-coil pickup closer to the bridge (like a J bass). This setup tends to offer more tone versatility.
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