Well, the similarities are that BOTH kinds were once much larger stars and are now about as close to "dead" as they can be. The main difference is one of mass...neutron stars have a HUGE amount of mass compared to the white dwarfs, and are usually the last physical remnant of a VERY massive star that went supernova. best example of one is at the center of the Crab Nebula...what remains is massive star compressed into the size of a city...it's rotates at a rate of 30+ revolutions per second and actually appears to blink on and off that frequently...this is also called a pulsar.. White dwarfs have far less mass and tend to be what remains from a star that became a red giant and expended all it had until it collapsed.....this will be the fate of our sun.