These two can confusing but they are actually to different things and very easy to understand
Independentely if the mail received on a mailbox is to be send internally (to another internal mailbox) or externally (to a mailbox from another domain) Mail Forward
is the correct choice if you want to send everything from the original mailbox to another mailbox
MAIL ALIAS is for instance if you have the mailbox email@example.com and create an alias named firstname.lastname@example.org or ConduRice@domain.com every message sent to either of the two
will end up in email@example.com
It's a matter of directioning, if you have a firstname.lastname@example.org and a email@example.com you will want to make a MAIL FORWARD from firstname.lastname@example.org to email@example.com, otherwise, if you use a MAIL ALIAS, any email sent to firstname.lastname@example.org will end up in email@example.com . Definitely not desirable.
So, in sum:
MAIL FORWARD from box1 to box2 when box2 is to receive contents of box1 but not the other way around.
MAIL ALIAS box1 with box2 when received mailed on either of the two will end up in both mailbox's