Are the two words synonyms? Is it grammatically correct to say "you have two choices, this or that?" Isn't that one choice? Should it not be "you have one choice, this or that" or "you have two options, this or that?". For two choices, don't you need a minimum of three options?
Choice: See 3a vs 3b & 4.
3a: a range of things that can be chosen
3b: one of the things that you can choose
4: the person or thing that someone chooses
Option See 2.
2: something that can be chosen : a choice or possibility
Note the the choice in case 4 is no longer strictly an option. (It has been chosen and no longer can be chosen.)
Host: We are giving you a choice now. You have three options - the envelope, the key, or what's behind the door.
Contestant: (Thinking - So many choices!) Okay I have made a decision. I have made my choice!
As nouns, "choices" = "options", but "choice" = "option" and "choice" = "options" are equally acceptable alternatives.
Host: But wait. Now that you made up your mind, I want you to consider this alternative...
Alternative: something that can be chosen instead of something else : a choice or option