From me looking at maps, excluding the Caspian sea and the Great Lakes, I see these in common for seas and lakes:
- Most are saltwater
- Connected to the rest of the ocean via either an isthmus, strait, river, or gulf
- Bigger and deeper than lakes
- Most are freshwater
- 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?