If a sailboat has the taller mast first it is a ketch, unless the second mast is behind the rudder post, then it is a yawl. If the second mast is taller it is a schooner.(When referring to modern sailboats and not tall ships)
Tallships with 2 masts are schooner, brig ,or brigantine .A brig has square sails on both masts. A brigantine has square sails on the foremast only.
If the aft mast is the taller it is a schooner , If the foreword mast is taller it is a ketch. If the aft mast is behind the steering post it is a Yawl
There are numerous classes of ships with two masts. Yawls, brigs, brigantines, ketches, schooners, and snows can all have two masts. Hull-type more determinative than number of masts.
Ketch or a yawl ,the ketch has the second mast or mizzen to the stern of the rudder stock. So the yawl has the opposite.