The two types of front suspension are independent, and dependent.
Independent suspension systems allow each wheel on the same axle to move up and down independently of the others, thanks to the use of either a struts or wishbone layout. This offers greater comfort and stability, as it can better deal with obstacles and unevenness in the road.
Dependent suspension systems, on the other hand, have all the wheels on an axle connected to each other, typically using a beam axle, leaf spring, or torsion bar setup. This makes for a more simplistic and less expensive design, but one that is not as able to deal with road imperfections as well as an independent system.