What is the Difference Between Factor Space and Equivalence Classes?

[commutator]

FACTOR SPACE is defined in my book as the set whose elements are the equivalence classes defined by the equivalence relation R .denoted by S/R

i cannot understand where this is different from equivalent class?
page 8 - a coursein modern mathematical physics - szekeres
any help will be highly appreciated.

 

[commutator]

understood. thanks.