Basically - you do not need "currentMillis" variable - use millis() function it its place.
Safer and "self documenting" that way.
Whilst it is not necessary to save the value of millis() in a variable it is good practice to do so.
(1) The name of the variable makes it obvious what the value represents
(2) Calling millis() several times in loop() is an overhead
(3) The value of miilis() may change during the execution of the loop() function but the value of the variable won't
(4) If a decision is based on the current value of millis() then if millis() is read again as part of the action then it may well read a different value because time has moved on.
SUMMARY :
It is good programming practice to save the value of millis() at the start of loop() and use the saved value throughout loop() for consistent timing and lowest overhead.