Leo on the inside, Sagittarius on the way in.
Your sun in Leo (fire, fixed) is the engine — what burns at the centre, what holds when you are at home in yourself. Your Sagittarius rising (fire, mutable, ruled by Jupiter) is the door — the way you arrive in a room, the first read the world takes of you, the body you walk in.
Strangers tend to assume you are fast and bold — that is the Sagittarius arriving first. Then they get to know you and discover the Leo fire underneath, which can be reinforcing — same flavour, more of it.
Reads as Sagittarius until you trust them; then Leo comes through. The fixed-mutable mix means you holds on the inside while adapts on the outside — internal and external rhythms are different, which is its own work.