"Better" is a simple adjective with a broad meaning. It is the comparative of "good." It means "more good." (Little children say "gooder" and need to be taught to say "better.")
"I think Honeycrisp apples taste better than Red Delicious apples."
"In my university's grading system, 'B' is a better grade than 'C.'"
"Newton realized that in a telescope, mirrors are better than lenses."
"Better off" is more limited. It always compares two life situations, two actions, two strategies.
"This restaurant specializes in seafood. You can get a steak here, but you would be better off ordering the salmon."
"You will be better off if you stay out of debt as much as possible."
"The country will be better off if candidate A wins then if candidate B wins."