I was all set to be cunningham's-lawed into telling you that's wrong about "travail", but holy shit, you're right:

https://www.etymonline.com/search?q=travail

Maybe I shouldn't be so surprised, since English still has the word "travails".

"Work" on the other hand means action, doing:

https://www.etymonline.com/search?q=work

That's quite a difference: one is something no one wants, and the other is something everyone does.

"Labor" falls on the "travail" side, meaning exertion, pain:

https://www.etymonline.com/search?q=labor