What are the conditions for an airfoil to be a "thin airfoil?"
There is no hard boundary. Normally it is around 8% relative thickness, details depending on camber and nose shape.

Typical for a thin airfoil is a stall originating from the nose, with a sudden separation of upper side flow, while thicker airfoils start to stall with a separation starting from the trailing edge and moving gradually forward. This gives thin airfoils a nasty stall behavior while thick airfoils stall in more benign ways. The stall behavior depends not only on thickness but also on camber and the geometry details of the airfoil nose, but can be used to separate thin from thick airfoils.

Thin airfoils make sense in two applications:


when the local angle of attack is well controlled, such as in flaps and turbo machinery, and
for trans- and supersonic flight where thickness causes wave drag.


In all other applications thicker airfoils with a blunter nose should be preferred because they allow to store more fuel and to make the load-carrying structure more efficient. The upper limit of practical airfoils is at 20% to 22%, the root thickness of the Davis wing as used in the B-24 and B-29.