What is the difference between 250K & 500K pots?
The first thing to establish is that we are talking about passive pickups as opposed to active pickups in this thread. Either 250K or 500K pots can be used with any passive pickups however the values of the pot used will affect tone slightly. The rule is: Using higher value pots (500K) will give the guitar a brighter sound and lower value pots (250K) will give the guitar a slightly warmer sound. This is because higher value pots put less of a load on the pickups which prevents treble frequencies from "bleeding" to ground through the pot and being lost.
This is why you will find that guitars with humbuckers like Les Pauls will opt to use 500K pots to retain more highs for a slightly brighter tone and guitars with single coils like Stratocasters and Adam's extensive collection of Telecasters will use 250K pots to add some warmth by slightly reducing the highs. You can also fine tune the sound by changing the pot values regardless of what pot value the guitar originally had. It is also worth noting that most pots have a 20% tolerance so that 500k pot may actually be anywhere from 400 - 600k!!
What is the difference between Audio and Linear taper pots?
Audio and Linear taper pots have the same total resistance but they differ in which position of rotation the pot will reach the 25%, 50% and 75% value as well as every other value between 0 and 100% . . Linear pots are usually marked with a B (examples 250KB, B250K and will reach 50% of its total resistance in the 50% rotation point. Audio taper pots are usually marked with an A (examples 500KA, A500K) and will decrease most of the resistance in the last 50% of the rotation. This can give a more gradual audio reduction is some cases. Some manufactures like Fender use Audio taper pots for both volume and tone controls. Gibson on the other hand uses linear taper pots for both volume and tone. And still others use Linear taper pots for volume and Audio taper pots for tone. However, if a problem of exists where a volume or tone pot has no effect on the sound, try changing the taper.
How to check the taper with an ohm meter: Set the pot to the center position (50% rotation) and measure the resistance between the center pin and each of the outer pins. If the the resistance is equal (50% of the pots value) the pot is linear. If the values are not equal, the pot is an Audio taper.