The ell is a unit of length and originates from historic England and uses the symbol ell.
The ell usually measured 45in or 1.143m but was origally a "cubit" - which was the length from your elbow to the tip of your fingers and literally translated from the word "arm". It was mostly used in the tailoring world when buying and selling textiles.
Although now obsolete, the word "ell" still survives in the English word "elbow".
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.