Single Coil or Humbucker? What is the real difference between the two?

Single coil pickups sound brighter and sharper. Their sound is characterized by the Fender Stratocaster and Telecaster models. A musical example would be the "skank" upbeat strokes in reggae music.

Humbucker pickups sound warmer, fatter, with more low end and less brightness. Musical examples would be any basic power-chord rock with lots of beefy low-end chords. Think AC/DC. When played clean without distortion, a humbucker pickup will tend to sound more appropriate for Jazz music.

A humbucker pickup is merely two single coil pickups side-by side, wired in opposite directions. The purpose of wiring them this way is to cancel out any external hum caused by nearby electrical equipment. A guitar pickup is more or less an electromagnetic antenna, and a single coil pickup that's near a 60-cycle electrical source (such as a computer monitor or a fluorescent light) will pick up that sound and amplify it.

Some versions of Fender-style guitars have had the option of a "stacked humbucker" which has the two coils stacked atop each other instead of side by side. This comes close to having the sound of a true single-coil while still having the noise rejection features of a humbucker.

Something very important you should know about humbuckers: Many guitars with humbuckers (such as my old Aria Pro guitar) have a switch called a coil tap which deactivates half of the humbucker, turning the guitar into a single-coil guitar with a flick of the switch. So I can go back and forth between single-coil and humbucker right in the middle of a song if I want to.

Finally, you might want to look into the Roland V-guitar system, which lets you turn any electric into any other electric+amp combination via sound modeling. Note that this is not a synthesizer system so it doesn't suffer from tracking delays... everything comes through including string scraping, feedback, whatever you can play, exactly as you play it. Got a cheap Japanese guitar, but you want to sound exactly like a Fender strat through a Marshall stack with Celestion 12's? Press a button and there you are. Want to sound exactly like Keith Richards on "Start Me Up", including the guitar, amp, and the nonstandard tuning? That's a named factory preset. Very much worth looking into if you've got the cash.