There are six different types of units, but you will never recruit special units, always nomads in general.
When you start a fight, you can decide how many of your nomads you will select for which type of unit.
The different units will become available to you, when you upgrade your clubhouse.
The fighting system is similar to the “rock-paper-scissors” system. Every type of unit is extremely superior over another and inferior to some others.
By looking at the colors of your units you will get an overview of how good the fighting strength of the selected unit is in comparison to other types of units. In the example above, your own unit is a “Cruiser” which is superior to the “Tourer” by 5:1 (see green color), but inferior to the “High Necker” by 1:5 (see red). On the left you can see the damage impact of your selected unit in comparison to the damage impact of your enemies unit (on the right).