According to GRRM, Jaqen was a bit influenced by his recent experience...
Jaqen refers to the Red God, and elsewhere to the god of fire. Is he referring to R'hllor? When we see Arya being educated by the Faceless Men, R'hllor doesn't seem to be particularly important to them.
(George thinks for a moment) Well, remember when Jaqen names him: he had very nearly burned to death recently...
ASSHAI.COM INTERVIEW IN BARCELONA - July 28, 2012
but the Many-Faced God is called because he represents all the other gods. There are roughly 30 statues of other gods in the House of Black and White.
"Then you have come to the wrong place. It is not for you to say who shall live and who shall die. That gift belongs to Him of Many Faces. We are but his servants, sworn to do his will."
"Oh." Arya glanced at the statues that stood along the walls, candles glimmering round their feet. "Which god is he?"
"Why, all of them," said the priest in black and white.
A Feast for Crows - Arya II
While on the other hand it seems the worshippers of R'hollor are intolerant of other religions, as evident by Mellisandre burning the effigies of the Seven.
The red woman walked round the fire three times, praying once in the speech of Asshai, once in High Valyrian, and once in the Common Tongue. Davos understood only the last. "R'hllor, come to us in our darkness," she called. "Lord of Light, we offer you these false gods, these seven who are one, and him the enemy. Take them and cast your light upon us, for the night is dark and full of terrors."
A Clash of Kings - Davos I
So in conclusion...
They do not worship the same gods.