A more in-depth explanation of vacuum forming is the following: a sheet of plastic is placed in a clamp frame (which holds the plastic sheet in place) and is drawn back into the machine over ovens to be heated, once the plastic is heated sufficiently, the machine brings the clamp frame forward back over the solid mold held in place below it. At that point, the mold is brought up underneath the heated plastic. The shape is formed as the plastic is suctioned (vacuumed) onto the mold. Fans above the fixture are turned on which cools the plastic. Once sufficiently cooled, the plastic with the formed part can then be removed. From here, the extra plastic surrounding the part must be trimmed off (most likely by band saw). Once only the part remains, it is de-burred (the rough edges of the plastic are taken off with a de-burring tool) to smooth the edges. Presto! Completed part.
Pressure forming is the process of taking a more complex, detailed mold and basically pushing it into the plastic (using pressure) in order to obtain the desired part. Pressure forming is great for producing parts with more detail.
Drape forming involves the same basic process as vacuum forming, however, drape forming involves cutting the plastic in the shape of the edge you want and then applying that heated plastic sheet to the mold. A fixture can be made to hold the plastic in place if needed.