They are used pretty interchangeably where I live. Like Alex said, some people also refer to the printed version with the noun "the printout."

"To print" is fairly universal and can be used to describe any action of printing. You could 'print out' in similar situations, but it isn't necessary to express it in that way in everyday usage. Alternatively, there is the noun 'a printout' which is from the verb phrase 'print out'. It references a printed version of something from a PC (document, spreadsheet, article, etc).

They are basically the same. But I think "print out" suggest that you want a physical copy. For instance, "My eyes get tired from reading the whole essay on the computer screen. Can you print it out for me?"