티 is a vibe, air, look, or feeling that someone gives off through their expression, tone, appearance etc. It is the basis of the following two expressions:
티(를) 내다 is an active form where someone is making their feelings apparent, and/or giving off an air or vibe:
화가 난 건 알겠는데 티 내지마!
I know you're angry, but don't show it!
왜 그렇게 티를 내니?
Why are you being so obvious?
그는 저를 좋아하는 티를 내요.
It's obvious that he likes me.
절대 티를 내지 않도록 노력해요.
Try not to make your feelings obvious.
남자들은 티를 잘 안 낸다고 했어요...
They say that men don't show their feelings...
선배 티를 내요.
He gives off that 'I'm your senior' vibe.
슬픈 티를 진짜 안 내려고 했어요.
I tried not to show my feelings of sadness.
짜증이 났는데 티를 낼 수 없었어요.
I was annoyed, but I couldn't show it.
티(가) 나다 is the passive form where the vibe or feeling can be seen or perceived by others:
얼굴에 티가 나요!
It's all over your face!
티가 나잖아!
It's sooo obvious!
진짜 화난 거 티가 나요.
You can tell that he's really angry.
부자인 거 티가 나요.
It's obvious that he's rich.
게으른 거 티가 나요.
He's lazy and it shows.
목소리에 화가 난 거 티가 났어요.
I could tell by your voice that you were angry.
왜 촌티가 나는 옷을 입고 있어요?
Why are you wearing clothes that give off 'country bumpkin' vibes?
화장 안 한 티가 나요?
Can you tell I'm not wearing makeup?
임신한 거 티가 날 리가 없어요.
You absolutely can't tell that she's pregnant.