According to the FDA, the term "bleaching" is permitted to be used only when the teeth can be whitened beyond their natural color. This applies strictly to products that contain bleach — typically hydrogen peroxide or carbamide peroxide.
The term "whitening," on the other hand, refers to restoring a tooth’s surface color by removing dirt and debris. So any product that cleans (like a toothpaste) is considered a whitener. Of course, the term whitening sounds better than bleaching, so it is more frequently used — even when describing products that contain bleach.