When to use congruent vs approximately?

What is the appropriate usage of the congruent ($\cong$) vs. the approximately ($\approx$) symbols?

• Shouldn't this be posted on the math page? Sep 28, 2013 at 1:22
• BTW, from en.wikipedia.org/wiki/Congruence, "Congruence, as opposed to approximation, is a relation which implies a species of equivalence." Sep 28, 2013 at 1:26

The notation $\cong$ corresponds to U+2245 APPROXIMATELY EQUAL TO “≅”, and $\approx$ corresponds to U+2248 ALMOST EQUAL TO “≈”. However, the Unicode names, written in all uppercase, are rather misleading here; and the names are really symbolic identifiers rather than normal names.
But from mathematics point of view, a $\cong$ implies equivalence of objects while a $\approx$ implies proximity of objects. More detailed explanation should be easy to find on the web.