True or false is different from HIGH or LOW right ?
Yes.
The if(variable == true) test is silly. If variable is true, the test evaluates to true == true, which is true. So, the initial test could simply have been if(variable). That is the convention for testing boolean variables. To do something when the variable contains false, you use if(!variable) (if not true).
For non-boolean variables, the 3rd and 4th examples are correct.