lhs == rhs returns True if lhs and rhs are identical.
lhs == rhs is used to represent a symbolic equation, to be manipulated using functions like Solve.
lhs == rhs returns True if lhs and rhs are identical expressions.
lhs == rhs returns False if lhs and rhs are determined to be unequal by comparisons between numbers or other raw data, such as strings.
Approximate numbers are considered equal if they differ in at most their last eight binary digits (roughly their last two decimal digits).
2 == 2. gives True.
== == gives True if all the are equal.
Equal[e] gives True.
For exact numeric quantities, Equal internally uses numerical approximations to establish inequality. This process can be affected by the setting of the global variable $MaxExtraPrecision.
In StandardForm and InputForm, lhs == rhs can be input as lhs \[Equal] rhs or lhs rhs.
It can also be input as lhs \[LongEqual] rhs or lhs rhs.
See The Mathematica Book: Section 1.5.5 and Section 1.5.6.
See also: SameQ, Unequal, KroneckerDelta, Order, Element.