Marque means brand/make. The main difference, and the reason “marque” is used today is the same reason as to why some companies call their liquids “vin de table”, and others “wine”.
Same with “dining alfresco”. It’s the posh term for “eating in the garden”.
That’s the reason why “marque” is connected to “posh” cars. Because it’s less pedestrian than “make” – it sounds more “exquisit”. It also requires a certain degree of history/pedigree. Tesla very certainly isn’t “marque”, it doesn’t have the heritage for it.
And yes, Mercedes is considered “marque”. Marque in particular refers to the three pointed star badge, not a specific model (marque is french for brand).
You can observe something similar in higher spec restaurants, where “sous vide” (sounds posh) just means “cooked in vacuum”. Or even more basic: “cuisine” instead of “style”, etc. You get the picture. Every car is “marque”, but only toffs advertise their cars as such. Technically, it applies to every (mainstream) manufacturer.