What is the difference between a check and a paycheck?
A paycheck is simply a check for your salary. It's just like a rent check, or a birthday check, or a grocery check... I've had "paychecks" that were personal checks from the owner of the business, I've had ones that are printed in the office I worked in and signed right there, and I've had paychecks that are printed through a third party company and mailed to me (my favorite, of course, is to forgo the "paycheck" entirely and get direct deposit :) ). Really, they're all just checks.
Although that's a little disingenuous, because banks are often slightly more trusting of paychecks. However, this has little to do with it being a "paycheck," per se, and more to do with the fact that they see you getting the same check for (roughly) the same amount on a regular basis; having seen you get a paycheck for the same amount from the same company for the last 12 months, there is less risk of the check bouncing or being returned unpaid, so you can often get banks to waive their hold policy and just give you the money.
There is little difference. A paycheck is a type of check used to pay wages. These days many people opt for direct deposit. So, the term paycheck can also refer to the payment itself:
1: a check in payment of wages or salary
2: wages, salary