The Cmaj scale and the Amin (natural minor) scale have the same notes. However this doesn't mean that the notes are used in the same way. The note A for instance sounds and functions completely differently in the two keys. It will sound colorful and perhaps even slightly unstable in Cmaj but will sound solid and foundational in Amin. When improvising, it can be useful to think in both scales from time to time, mixing the Amin scale with the key of Cmaj and vice versa. Even though they contain the same pitches, the melodies you will come up with will be completely different.
For instance, when I'm in Cmaj, I might decide to think and play in these scales to name a few:
Although none of the scales after Cmaj introduce ANY new pitches, each of them gives a different sound and color. Depending on style on context some of these may be more appropriate than others, so use your ear to tell you whether it sounds good.
One word of caution. I do not recommend ignoring mastery of the Amin scale just because it contains the same notes as Cmaj, which allows you to get by knowing just the one scale. This will greatly inhibit your ability to think in a certain key and to come up with varied ideas in that key. So, in short, learn all the scales and decide how YOU want to use them.