Bee, sounds like the oregano we grow. We grow a large amount in a sunny spot, because the wild bees love the flowers. I have not been able to identify the variety and I have forgotten where we first obtained it some 40 or so years ago. It is perennial, but needs renewing every two-three years from seed or divisions.

Dried Greek oregano is available here in large jars, from Real Canadian Superstore. It is good, but we prefer the Mexican, which seems more aromatic, and has a different flavor. There are 2-3 other species, also growing in Greece and the Mediterranean area.
The Greek is Oreganum vulgare hirtum.
Mexican oregano is an entirely different species of plant, Lippia graveolens.

Two or three other aromatic plants used as herbs or medicines are also called 'oregano,' but they are all unrelated. Not easy to know what you are getting in the herb-medicinal market.