A flat dish end (or "head") is self-explanatory. A (hemi)spherical dish end also. If you slice a vessel in half along its axis, you get a cross-sectional view. The flat head is a straight line (or strip). The hemispherical head's cross-section is a semicircle. The (semi)elliptical head's cross-section is half an ellipse; usually the minor axis is half the major, hence the term 2:1 elliptical head. Usually such a head also includes a cylindrical skirt (band) about 2 inches (50 mm) wide all around. A torispherical head consists of a spherical cap (of radius about equal to the vessel diameter) spanning about 80% of the vessel diameter, with a circular arc (called the "knuckle") on either side, blending into a cylindrical skirt. This knuckle arc, when revolved about the axis, forms part of a torus, hence the name "torispherical" for the whole head.
As I recall, the ASME Boiler and Pressure Vessel Code has pictures of these along with the formulas for calculating proper thickness-pressure relationships. Perhaps surprisingly, the elliptical ones are the easiest.
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In vino veritas; in cervisia carmen; in aqua E. coli.