Oxygen bleaches are color safe, and are marketed as such. Some laundry detergents contain an oxygen bleach. I find them useless because of their weakness. When a garment tag instructs not to bleach, that means chlorine bleach. Oxygen bleach is safe to use.
Chlorine bleach is a strong oxidizer.
It whitens by bleaching the color out of stains, soil, and build-up. It will also bleach the dyes in non-colorfast garments, ruining them. It sanitizes by literally burning up germs. Too much chlorine bleach will actually burn away at the cloth itself, weakening it and even causing it to rip and fall apart. It can also easily irritate your skin and cause chemical burns.