Great question - unfortunately, no good answers.
Just looking at Fender (a lot of other builders make "P" basses as well) you'll find as many exceptions as there are rules.
Just for giggles, looking at Fender's current website:
- at least 7 different pickup configurations for a P bass
- one body style for a P bass (balanced vs offset like a Jazz) although there used to be a P bass Plus with a different body shape
- two different headstock shapes
- four and five string options
- at least 4 different pickguard shapes
- 20 frets, not sure if there have ever been more or less frets available on a fretted fender p bass in the past
- block and bound necks, dot necks, fretless necks
- tons of different control layouts
- 2, 4 and 5 saddle bridges
- standard and narrow or jazz neck widths
- they currently all have clover leaf tuning keys but in the late 1960's some had lollypop keys
So it seems the only thing that might be consistant among current P basses is 20 frets and clover leaf tuning keys but I don't think anyone would define a P bass using those terms.
This is what most people consider a P bass to look like and it does have a distinctive sound and feel vs Jazz basses or other non traditional P basses that might have humbuckers or other pickups or control layouts or neck sizes.
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