Both words descend from the same Arabic root, both practices involve turning, and both belong to Anatolia, so outsiders have been running them together for a long time. The two are not the same thing, and Alevis say so plainly.
The Mevlevi sema is performed by trained dervishes of a Sufi order, in a purpose built hall, under a formal ceremonial that the order maintains and teaches, to an ensemble led by the reed flute, and the turning is done by men in a fixed and instantly recognisable costume. The semah is performed inside the cem, the Alevi communal ritual, by ordinary members of the congregation rather than by an order, with men and women turning together, to the saz. It is not staged, it is not a discipline entered by initiation into a Sufi lineage, and it does not belong to a hall the way the sema does.
The difference that matters most is what the practice is for. The sema is one order's method. The semah is a constituent duty of a congregational ritual in which the entire community takes part, and it sits inside a service that also settles disputes, hears confession of wrongs and shares food. Attaching Alevism to the Mevlevi rite because both turn would misdescribe a whole tradition's worship in order to fill a gap, which is why the atlas holds them as separate entities and links them only as related practices. Mixed participation in particular has been used as a charge against Alevis by hostile neighbours for centuries, so the point is not academic.