My first guess would be that your Finale document has both a score and a generated linked part.

Perhaps you edited the score, and printed the linked part? - or edited the part, and printed the score?

"On my screen everything looks great. I hit print and the measures are not in the same locations as they are on my screen."

If this statement is true as read, you have a problem with your printer. I would first re-install your printer. Reboot your computer, too. Let's eliminate that first off. If your printer is printing other documents OK than you do have something going awry with Finale. In the Finale print box make sure you have checked the same thing you are viewing on screen. If you are viewing the score than the score box should be checked, etc.

If this looks OK, I would re-install Finale.

If you are printing to a PDF printer or from a PDF printer, you need to re-install it. It is corrupted.

If none of this helps, come back but explain the exact details of how you are trying to print.

I've used Finale PrintMusic 2014 with all of my other songs. I just purchased Finale 27 and this is the first song I've typed in from scratch. (The others I moved over from the 2014 version.) So when I saw the word 'score' on a piano piece I was a bit confused and figured I just did something wrong in the wizard thingybobber. So I unchecked that box when I printed. I just checked it and printed and it looks like my screen!!!  Thank you so much. You guys are great!

Great!