"Is there any difference in using the following phrases:" <--- this is the phrase you need. :) "Important things" is exactly as you understand it. The things are a priority, or have major value. "Urgent matters" means the things need to be dealt with as soon as possible. You have a time factor here. Using "businesses" in this context is wrong. Check the use of countable/uncountable nouns. It's more natural to say, "I had some urgent business (to attend to)."

Important is used to describe something that is significant and is to be considered ahead of other things. "Reading is important to me." 'Urgent' is used to describe something that needs to be done as soon as possible. Time is a large factor. "It is urgent that we ship this today." If I say that reading is important to me, it is not necessarily urgent - I don't have to do it now.