``Pressure'' is a general term meaning force per unit area, for any force which is distributed over a surface. It can apply to solid objects as well as fluids. For an object immersed in a fluid, there's a contact force exerted by the fluid on all surfaces of the object. Since this fluid contact force is a distributed force, it's called a pressure. For a static situation, the pressure force is normal to every interface.
``Buoyancy'' is a more specific term. It refers to the net force experienced by an object immersed in a fluid due to contact with the fluid. Its origin is the difference in pressure between the top and bottom of an object. The bottom of an object is deeper (farther from the surface), and hence the pressure is higher on the bottom than the top, by Pascal's law- this leads to a net buoyant force on the object upward from pressure (the overall net force, including gravity, may be upward or downward, depending on mass of the object). The buoyant force on a object is proportional to the volume displaced, according to Archimedes' principle.