Agate is chalcedony with visible banding, and the banding is what distinguishes it from plain chalcedony or jasper. Most red agate sold commercially has been heated: the heat deepens and evens out the colour, and it is permanent. It is a standard treatment and not a fake, but it is also not "natural colour," so it is stated here rather than left ambiguous.
The marking to look for on dyed rather than heated stone is colour pooling in cracks, which heated material does not show. Beads are 8 to 12 mm; the larger sizes are noticeably heavier on the wrist.