Traditionally, a diptych is a pair of paintings or carvings on two panels, and usually hinged like a book. Diptychs are known from the Roman period.
Modern artists today use the term to mean two pictures not connected to each other but designed to hang together as a pair. These could be individually framed pieces hung close together on a wall, or two pieces placed in a two-panel mat in the one frame.
Traditionally, a triptych comprises a painting in three sections, or three carved panels, joined with hinges and which can be folded shut or displayed open. Triptychs made popular altarpieces from the Middle Ages on.
As with diptychs, modern artists today use the term to mean three pieces of artwork not joined to each other but designed to display together. Again as with diptychs, these could be individually framed but displayed together, or all in the one frame with a three-panel mat.