When to use Ln(1+HPR) and when to use E^rcc?

I’m having a bit of confusing correctly identifyinf when to use each one. Do both give you continuously compounded rates of return? Or is one solely used to convert a continuous return to a stated type of return? Is e^rcc only used for given annual stated rates and turning them into continuously cpounded rates? And is Ln(1+HPR) then only used when given a HPR for say, 5 months and you want to see the continuous compounded rate of return over that same time? The problem i’m having is that Ln and E^ are giving higher/lower results, so I’m having trouble figuring out when to apply each one. Thanks in advance!

Ln(1+HPR) is for calculating continuously compounded return for that holding period. e^rcc is the opposite. Once you have continuously compounded return rate, you use this to work out the 1+ HPR. E.g. HPR = 5% --> CC = ln 1.05 = 4,87% CC = 4,87% --> e^4,87% gives you back 1.05

adding to this - for one year HPR = EAR here

Thanks elcfa and hkalra32, its much clearer now!