What’s the actual difference between retro games and classic games?

I see these terms used like they mean the same thing, but I don’t think they always do.

From how I understand it:

Classic games are titles that became important, iconic, or timeless because of their quality, influence, or reputation. They can be old, but the main point is that they’re widely respected and still remembered. A game can be called a classic because it defined a genre or stayed relevant for years.

Retro games usually refers more to the era, hardware, and style. These are older games from previous console or PC generations, often associated with pixel graphics, chiptune music, arcade design, cartridge systems, and older technical limitations.

So in my head:

• every retro game is old enough to belong to an earlier era
• not every retro game is a classic
• every classic game is respected
• but not every classic has to feel “retro” in the same way

For example, a random PS1 game might be retro, but not a classic.
A game like Super Mario Bros. or Chrono Trigger would probably be both.

Would you say the difference is mainly:

• quality and legacy for “classic”
• age, era, and style for “retro”

Or do you use the words differently?