Seeing as how this is always a somewhat ambigious thing I thought I'd clarify how these both work, at least for this game.
Taking 10
You can take 10 at any point when not in combat rounds, you may only take 10 on a skill in which you have ranks. Taking 10 represents something you've done so much that it's pretty much become second nature. Think of this like climbing a fence, when you were a kid, it took you a while to figure out how to find the right handholds and the right way to position your feet when hopping over but as an adult, you can scale that fence with little to no difficulty. Taking 10 is the Realization of "Practice makes Perfect"
Taking 20
Taking 20 represents not the utmost care and precision, but actually persistence. Anytime the failure of a skill would have consequences beyond time consumed you cannot take 20 (except under special circumstances).
You can take 20 on...
Perception (Search) Checks
Knowledge (Research) Checks (Requires a Library or other large source of information)
*Craft or Profession Checks
*When you take 20 while crafting an item you must pay the cost x2 to represent the failures you are unable to sell for partial cost