My Mac only has thunderbolt connections. Do they make a external drive with thunderbolt connections? Or do I have to buy an adaptor too?

Depending on the speed that you're willing to pay for (i.e., how expensive a drive you want), you should be able to use any external drive that comes with a USB-C cable without using any adapter.

(And note that USB 4 and USB 3.1 are both backward compatible)

Also see the following from MacBook Air - Technical Specifications - Apple

Two Thunderbolt / USB 4 ports with support for:

• Charging
• DisplayPort
• Thunderbolt 3 (up to 40Gb/s)
• USB 4 (up to 40Gb/s)
• USB 3.1 Gen 2 (up to 10Gb/s)

An external drive with a USB-C connector will work just fine with the Thunderbolt ports on your Mac. This is what I use on my Mac.