Current sources of information are those that have been written very recently. Examples of current sources are an article about the latest in cataract surgery or a book written recently about Abraham Lincoln. To determine if something is current, look at the date and see if it was written recently. How recent is recent enough to be considered current? Well, that depends on what the information is and how you will be using it. Would you want your health care professional to be reading a seven year old article about cataract surgery? But, a seven year old article revealing how Lincoln worked with his cabinet to find unity would be current enough to use in an academic paper.
Contemporary sources of information were written at the time of the event. To determine if something is contemporary, look to see if it was written at or near the time of the event. Alexander Hamilton (1755-1804) of Broadway musical fame, Eli Whitney who invented the cotton gin, Paul Revere who warned that the British were coming and the creation of the United States Post Office are contemporaries: they all happened/existed at the same time.
So we need to ask ourselves lots of things before we sit down at a computer. What are your questions and what kind of information source will answer them? Do you need a full book, a brief encyclopedia entry and/or several articles? How current do you need the information? Do you need scholarly information or will popular information suffice? Having a clear understanding of what you need means you have a clear idea for what to look. That will save you time.