When you deal with NULL in SQL Server you basically work with 3-value logic with all the implications.
IF(@myVar != null) vs IF(@myVar is not null)
It basically boils down to the question
what is the difference between: @myVar = null vs @myVar is null
@myVar = null will always evaluate to null as what you are asking is: is the value in @myVar equal to UNKNOWN
As you do not know what the UNKNOWN is this question cannot by answered yes, or no so it evaluates to UNKNOWN
e.g.
"is 1 = UNKNOWN" - I do not know
"is 'a' = UNKNOWN" - I do not know
"is UNKNOWN = UNKNOWN" - I do not know
"is 1 = UNKNOWN" - I do not know
"is 'a' = UNKNOWN" - I do not know
"is UNKNOWN = UNKNOWN" - I do not know
The last one may be a bit tricky but just imagine that you have 2 boxes with candy and you do not know neither how many candy are in box1 one nor in box2 so asking.
so the answer is I do not know
the second one @myVar is null is different as it is like asking is the value in @myVar UNKNOWN
so the difference is that you specifically ask "is it true that the value stored in the variable is UNKNOWN?", so
"is 1 UNKNOWN" - NO
"is 'a' UNKNOWN" - NO
"is UNKNOWN UNKNOWN" - YES
"is 'a' UNKNOWN" - NO
"is UNKNOWN UNKNOWN" - YES