Hi, Bigsallysmom,
No, these are ebooks that have the price set to $0.00 for a period of time (a day or more). Authors do this to gain reviews or to get readers hooked on a series.
It does pay to make sure the book you are about to "buy" is STILL shown with a price of $0.00 -- to make sure the promotional price of FREE is still in effect.
Don't confuse the $0.00 price of a free book that is on promotion with the "Read for Free" button that is connected to Amazon's reading club thatur you pay to join.
You are right that when you are a Prime member, you can "borrow" books for free. I think you get two weeks or something like that to read the book, then it disappears from your archive. Again, this is a different thing than the free ebooks where the author has set the price temporarily to zero.
Simply look at the "Kindle edition price" near where you click to "Buy it" and make sure it is $0.00. You'll get an order acknowledgement as if you paid money but it will show you spent zero.