It is called Sex-Linked Red as only the female cat can have 2 Red alleles. Male cats can only have one Red allele. This is because the gene lies on the XY pair of chromosomes that determine what the sex of an animal is.
Imagine the Red gene on the bit of the X shape that does not appear on the Y shape.
So a Red male (XY) has one Red allele and a “blank” (O-), a Red female (XX) has 2 (OO) and a Tortie has one Red allele, and one recessive Non-Red allele (Oo). Therefore in a Tortie there is Red and the Full Colour showing on her as the non-recessive allele (o) lets the full colour gene shows up. I think I’m right in saying that this sex-linked colour phenomenon is unique to cats and is because alleles are on the X chromosome only.
So a sex-linked Red cat still has the 2 alleles for Black, Chocolate and/or Sorrel in its genetic makeup. BUT the action of the sex-linked Red gene is to change the melanin pigment that causes the Black/Choc/Sorrel colour. It turns it into another sort of melanin that gives the colour Red.
A Red cat will “carry” 2 full colour alleles like any other cat.
If you want to breed a Tortoiseshell cat you can use any colour of female Abyssinian apart from a Red, and breed to a Red or Cream Male.