Solid does not wear an eyepatch
Sure, he does, look!
But you're right on all other counts. I have no excuse for now knowing what's going on other than that the games come out 5 years apart, the two main protagonists look very similar, and the chronology jumps around a lot so that ages are hard to keep track of, and somehow Kiefer Sutherland got involved (give it 5 more years, and Troy Baker will get involved).
I considered playing the games in chronological order, but I decided I'd rather be re-introduced to the characters in their canonical order, and experience a gradual gaining in fidelity of the games.
I just finished Metal Gear 2: Solid Snake. I now know that Big Boss was Snake's former commander, and is one of those "war-is-all-we-know" trope-types. Up next is Metal Gear Solid, which I think I'm looking forward to most of all.