What is a difference between EAR and continuous compounding?

The continuous compounding is a version of the EAR where the number of compounding periods goes to infinity i.e. it is compounded continuously, for example, every split second. So for continuous compounding we use the formula:

PV x e^(r x N), where r is the stated rate and N is the number of years, we would use this if we are told explicitly that the number of compounding periods is infinity i.e continuously compounded. Pressing 2nd LN, gets access to the e function of the calculator.