Open the Touchpad module in System Settings and move to the Touchpad information page.

The bold centered text shows the product name of the touchpad.

The line right below the name tells you, how many separate fingers are detected by your touchpad during taps. Most touchpads will only detect a single finger, but modern or expensive laptops (e.g. MacBook laptops from Apple Inc.™) will have better touchpads.

The Buttons box tells you, how many buttons your touchpad has. You might notice, that even if your touchpad physically only has left mouse button and right mouse button, the middle mouse button is also checked. In this case, you can reach the middle mouse button by pressing left mouse button and right mouse button at the same time.