The classic game matching "move pieces from your base into opponent's base" is Chinese Checkers (or its predecessor Halma). Checkers/Draughts is about capture, not base transfer. Here's the distinction.
If your game has a star board, marbles, and hopping to the opposite point — it's Chinese Checkers. If it's a square grid with orthogonal hops — it's Halma. If it's diagonal jumps capturing on an 8x8 board — it's Checkers.