The point is a unit of length in the field of typography and uses the symbol pt.
It is the smallest unit in the world of typography. There are 12 points in a pica.
In physical printing methods / press systems, the point size is the height of the metal press body on which the font's letters are made. When applied to the digital type space, letters are designed around a theoretical size, an em square which is scaled to the relative point size (when specified of course!).
The em is a unit of length in the field of typography and uses the symbol em.
It is a "relative" unit and equals the currently specified point size. For example, 1 em in a 24-point typeface is equal to 24 points. This allows a typographer to specify text size relative to a base figure.
In metal type, the em was equal to the line height of the metal body. This meant the physical size of the letter could not exceed the em. In digital type, the em is a grid of arbitrary resolution so can be scaled to any point size for screen or print.