If something costs $7,987, I may say it's approximately $8,000. It means that it's a number close to the actual. I may or may not know its EXACT value, but I can be very close.
If I'm not sure of something's value, but I make my best guess, then I have estimated its value.
It doematter. As the previous post explains, you should only use estimate if you don't know or can't know the exact figure. Estimation is a best guess, which either is exactly correct or is wrong. Approximation is not a guess, but an assertion of fact. For example: a rounded number, which is a correct approximation if it is merely close.