Take 20 assumes taking 20 attempts and 20x the time, generally using brute force things. You're going to fail over an over before you succeed, so it's only used on tasks with no consequence of failure (For example, Escape Artist to get out of ropes binds in an unguarded room)
As a comparison, it's like practicing for a Long Jump personal best, repeatedly performing the task, sometimes botching your jumps, sometimes getting alright results, but eventually making it after enough attempts.
Taking 10 assumes one careful attempt without taking much risks, with time to concentrate and focus on the task (not being threatened). For example, say your long jump personal best is 6m, and there's you're standing in front of a pit that's 4m across and has spikes at the bottom.
Instead of getting the fastest, best runup you can, sacrificing control, you go a little slower, control your movement, and take one good leap that hasn't got the power to get you anywhere near your record, but dosen't have the chance of slipping up, tripping, or otherwise blundering and falling to your death, whilst having enough distance to clear the gap. It makes no difference if you make it by half a meter or two whole ones. It does make a difference if you don't make it.