In the above mentioned sentences, yes, all meanings are the same. Even if you check the dictionaries you will see that find out means to discover and vice versa. So, basically they are synonyms apart from very few instances or cases that, in order to be very exact, you would need to use either one or the other:
E.x.: Archaeologists discovered important treasures in the area.
-He is on a trip.
-Really? How did you find out?