Is the expression a || b the same as a & & ! b

Most definitely not! A || B is A OR B, if A is true OR B is true, the statement will be true. A && !B is A AND !B, only if A is true AND B is false will the statement be true. With OR, B can be true and the statement will pass.

You could test it
case (1)
a =true, b=false
true || false    = true
true && !false = true
PASSED! 

a=false b= true
false || true     = true
false && !true = false
FAILED!

also try a=true, b =true

so the it is not the same