The most common variety is Thymus vulgaris. Thyme is of the genus Thymus of the mint family (Lamiaceae), and a relative of the oregano genus Origanum. We use it in Egypt with chicken and pizza, used in ancient Egypt.
Several Thymus species may occur in the Moroccan Atlas including: Thymus algeriensis Boiss. & Reut., Thymus maroccanus Ball, Thymus saturejoides Cosson, and Thymus serpyllum L. You might also contact someone from the Moroccan-based Arab Federation of Medicinal and Aromatic Plants: http://fapam.um5s.ac.ma/
If it is different from what you find in the market, t should be Thymus algeriensis Boiss. & Reut. If you perform essential oil extraction and you find major compound is thymol versus carvacrol, so it is definitely Thymus algeriensis (see my paper for reference)
To confirm the genus, you should consult a botanist or validation.