For a language $L$
If there is some Turing Machine that accepts every string in $L$ and rejects every string not in $L$, then $L$ is a decidable language.
if there is some Turing machine that accepts every string in $L$ and either rejects or loops on every string not in $L$, then $L$ is Semi-decidable or recursive enumerable(RE) or computably enumerable (CE).
Semi-decidable means "Recursive enumerable".
Undecidable means "Not REC"
Semi-Decidable And Undecidable means "RE but Not REC"