These two products are the same in the sense that both are conditioning products designed to keep your beard hair healthy. That's kind of where the similarities end though - beard softener is meant to be used in the shower after you use beard wash. *Pro tip: If you want to do a deep condition for your beard, leave the softener in for a few extra minutes.
Beard oil is built to work almost like a leave-in conditioner. While your pores are still open after your warm shower, apply it to not only your beard, but the skin underneath to keep both your hair and your skin soft, hydrated, and conditioned.
How you combine these products and how often you use them is really up to you - some guys prefer using a softener every day, Eric prefers using it only on the days he washes his beard with a beard wash. Oils can be used daily or only on wash days. It's really about finding out what works for you and what you prefer.