Why are the Great Lakes not considered a sea? From me looking at maps, excluding the Caspian sea and the Great Lakes, I see these in common for seas and lakes:

Seas


Most are saltwater
Connected to the rest of the ocean via either an isthmus, strait, river, or
gulf
Bigger and deeper than lakes


Lakes


Most are freshwater
Landlocked
Not nearly as big or deep as any sea


So back to these 2 bodies of water in question. Some people consider the Caspian sea to be a lake and others consider it to be a sea. While historically, it might have been part of a sea, it is landlocked now so it would be more suited to call this the Caspian Salt Lake, thus making it the largest lake on Earth and also the largest saline lake.

The Great Lakes are also in question, to me at least. While the majority of the world considers them lakes and they were historically a lake (really, the rivers and small lakes in that area connecting them are so small in comparison that it is basically 1 body of water), the Erie canal has since then connected the lakes to the St. Lawrence River. So it would be more suited to call this the Great Freshwater Sea. I have no idea how this would rank up to other seas like the Mediterranean Sea in area but it would be one of the world's few freshwater seas (Joining the Sea of Galilee).

So why are the Great Lakes not considered a freshwater sea when other than the freshwater, they are essentially like any other sea?
"Sea" versus "lake" versus "just part of the ocean" is a bit fuzzy, but there are two things that are universal about seas:


They are saline.
They are either endorheic or have a sea-level (tidally-influenced) connection to the ocean.


Now, let's see how the Great Lakes look under these criteria.


Saline?  No, salinity is 0, give or take measurement error.  Even the Baltic Sea, the least-salty of the generally-recognized seas, is far more saline, at 0.5%.
Endorheic?  No, they're connected to the ocean by way of the Saint Lawrence River, and have been for at least 10,000 years.
Sea-level connection?  No, the Saint Lawrence River has about 500 km of non-tidal flow below the outlet of Lake Ontario, over which it descends 75 meters.


Score: 0 out of 3.  Not surprising that the Great Lakes are considered lakes, not seas.