Tie" means attach or fasten with string or similar cord. And "tie up" means a link or connection especially one between commercial companies

I am from central United States. Tie is using string. A hat has strings so that you may tie it to your head. Tie up is to restrict someone's movement by binding their hands and feet with rope. A dog can be tied up to a tree. A criminal might tie up a prisoner. If I am unable to move in a traffic jamb, I might sat I was tied up in bad traffic.

Suhaq is correct. However, most of the time 'tie' and 'tie up' mean basically the same thing and are interchangable. Additionally, a 'tie-up' is also a British term for what Americans and many others call a 'traffic jam' or a situation where traffic moves very slowly and/or is snarled. In another sense, saying you are 'tying-up' somethings means that you are bringing something to a conclusion/completion or putting the final and finishing touches on it.