well, here are a couple of examples, although I don't know that it would ever be wrong to use = when you mean equivalent. y = ax + b [this is an "assignment" which is typical for "="] a + b == b + a [this is not an assignment but a statement of equivalence]
Use ##\equiv## for equations that are identically true, such as (x + 1)^{2} ##\equiv## x^{2} + 2x + 1 and sin^{2}(x) + cos^{2}(x) ##\equiv## 1. Each of these equations is true for any real x. Use = for equations that are conditionally true, such as 2x + 1 = 5. This equation is true only for x = 2; i.e., only under certain conditions.