> In the Paleogene and Neogene Periods (~66 million to ~1.8 million years ago), the mountain chains that today constitute the Atlas were uplifted, as the land masses of Europe and Africa collided at the southern end of the Iberian Peninsula.

But it also notes,

> The Anti-Atlas Mountains are believed to have originally been formed as part of the Alleghenian orogeny. These mountains were formed when Africa and America collided

Anti-Atlas? If we jump over to the Anti-Atlas article we see,

> In some contexts, the Anti-Atlas is considered separate from the Atlas Mountains system, as the prefix "anti" (i.e. opposite) implies.

and

> The summits of the Anti-Atlas reach average heights of 2,500–2,700 m (8,200–8,900 ft),

So in addition to subsequent events, the portion of the Atlas originally formed with the Appalachian is geologically distinguishable from the other portions of the Atlas chain, and actually significantly lower than the parts of the chain formed later, though not as low as the Appalachians.

The collision with Asia began around 50–55 Ma and is still ongoing, which is why the Himalayas are still rising today.