Retain VS remain

We have had a question about the difference between “Retain” and “Remain”. Here are my notes:

To continue to hold; to keep in possession; to not lose or part with

Can be used as a synonym for “Persist”

1. To continue in the same state or condition: “These matters remain in doubt”. (Describing status)
2. To continue to be in the same place; stay or stay behind: “We are remaining at home”. (Physical Position)
3. To be left after the removal, loss, passage, or destruction of others: “Only a few trees remain”. (Left over)
4. To be left as still to be dealt with: “A cure remains to be found”.
This indicates that the search continues

Remain is generally NOT used when you mean “Persist”.
It is used when describing NO change in physical position OR┬áto describe what is “left over”, RATHER than what continues or is maintained.