Remake vs Sequel

what is the difference between a remake and a sequel ?

A remake is a new movie using the same story but with a different cast; a sequel is a movie in which the story of the 1st movie continues, with or without the same cast.

Anna and the King (1999) is a remake of The King and I (1956).
Toy Story 3 is a sequel to Toy Story 2.

is there any difference between sequel and series
thanks for your prompt reply

Series are for TV; they are planned as such and run for many shows.

thank you