Prime Reading and Kindle Unlimited are very similar in terms of how you use and enjoy books. But there are a couple key differences. Prime Reading is a benefit of a Prime membership ($119 a year) and gives you access to one free book from the Kindle Unlimited library each month. The available books rotate in and out. Kindle Unlimited is a separate service for $10 a month (currently with a two-month free trial) where you can borrow as many as you like (ebooks, audios, magazines) with no due dates and can hold up to 10 at a time.
Both are great deals for bibliophiles but if you are balking at subscribing to yet one more service and already have Prime (like over 65% of Americans!) than 12 free books a year is still a good deal and can further help you recoup the cost of that 2-day shipping membership.