Should they be marked as synonyms?
word-difference: you ask for the difference between words
word-choice: you ask which word you should use in a specific context
The emphasis can be very different. With "word-choice" you can ask opinion about if the word is uzinda or is useable in a specific context. "word-difference" is much more about the meaning, and not the usability and uzindability.
Clearly, since Stack Exchange sites expect well-scoped questions, I would generally expect word-difference questions to make clear in which context the OP is asking; questions should not be about the difference between two words in general, since that would probably make the question too broad and less or no helpful to future users (which is the target of any Stack Exchange site, together the user who asked the question).
In the same way, word-choice question should not ask for choosing a word from the full dictionary; the OP should make clear which words they think could be used.