Clips are basically a metal clip (hoho) used to conveniently load a column of individual cartridges into the magazine, which is what actively stores and then feeds ammunition into the barrel for firing.
On modern assault and battle rifles, the magazine is similar to a clip in that individual rounds are loaded into it prior to the magazine being inserted into the magazine well under the firing chamber. The difference is that while a clip is simply helpful for storing ammunition and loading a weapon, an external magazine is an essential, albeit removable, part of the weapon.