From the Game Manual / Box:
With Gradius 3 & 4 you get two shooting games on one disc! Gradius 3 starts with a dazzling intro movie and then settles into a side-scrolling shooter. You must shoot your way against numerous alien ships hurtling toward you while picking up different power-ups--such as speed tune-ups, missile weapons, lasers, and shields--to keep your end up in an ever more intense battle. Also, you can pick up the husks of burned-out foes for more rewards.
Gradius 4 is essentially the same type of game, but the side-scrolling action often breaks up and allows you to move in less restrictive ways. Of course, that newfound freedom doesn't necessarily work to your advantage; wild enemies can now come sweeping at you from all angles.