Yeh be careful with that, I found out the hard way.
1.50 / 1.75 (standard typical BMX pro size) rims are approx 406mm and 1-1/8 / 1-3/8 (mini / junior) rims are approx 451mm. (I think this measurement corresponds to the tire bead.)
So frame sizes and especially tire, tube and brake sizes are different. You can be lucky and get away with frame size (ie fit a 1-3/8 wheel to a standard 20" frame), but you'd need to play around a bit to get the brakes to line up. If you're talking about new school race then LDC brakes have enough adjustment to cover both sizes.