There are various. The eggs, the mouthparts (adults), the contact to the water surface (pupae), the respiratory (larvae), just to name a few, which are mentioned in different keys. Indeed, the antennae are useful, too.
From Thielmann & Hunter (2007):
-Scutellum rounded with setae evenly distributed; palpi about as long as proboscis --> Anopheles
-Scutellum trilobed with setae confined to three groups; palpi shorter than proboscis --> Aedes
First make sure you are observing a female mosquito (they have simpler antennae).
If you are looking at the adult, the easiest way to determine an Anopheles is if they have long palps (about the same size as the proboscis).
If they have short palps, that does not necessarily make them an Aedes mosquito. To determine that, look at the end of the abdomen. If the abdomen is pointed with short palps, you most likely have an Aedes mosquito. It could also be a Psorophora mosquito, but those are usually very easy to spot.
If the abdomen is blunt you are most likely looking at a Culex mosquito.
I recommend using a key if you have several mosquitoes to differentiate.
The colleagues have described some physical features but I would add that several Anopheles species are active in malaria transmission, tend to have an activity peak between dusk and down, and have a more zoonophilic behavior while Aedes species include more dengue, zika, and chikungunya vectors. The repose posture of both genus could also pose differences.