What are the differences between types I, II, and III emergency doors? What are the differences between types I, II, and III emergency doors?
The major difference is size.
FAR part 25.801 defines them as:

(1) Type I. This type is a floor-level exit with a rectangular opening
of not less than 24 inches wide by 48 inches high, with corner radii
not greater than eight inches.
(2) Type II. This type is a rectangular
opening of not less than 20 inches wide by 44 inches high, with corner
radii not greater than seven inches. Type II exits must be floor-level
exits unless located over the wing, in which case they must not have a
step-up inside the airplane of more than 10 inches nor a step-down
outside the airplane of more than 17 inches.
(3) Type III. This type
is a rectangular opening of not less than 20 inches wide by 36 inches
high with corner radii not greater than seven inches, and with a
step-up inside the airplane of not more than 20 inches. If the exit is
located over the wing, the step-down outside the airplane may not
exceed 27 inches.

There is also a type IV:

(4) Type IV. This type is a rectangular opening of not less than 19
inches wide by 26 inches high, with corner radii not greater than 6.3
inches, located over the wing, with a step-up inside the airplane of
not more than 29 inches and a step-down outside the airplane of not
more than 36 inches.

If you read the full text, you will also find definitions for ventral and tailcone exits. For pictures I refer you to this answer.