(b) is stating a certain fact.
People will use the (a) sentence more vaguely, or when there is still uncertainty.
Consider these sentences. They present a similar difference in meaning, and some people that are very particular about English (like grade school English teachers) will point out the difference:
(c) Could/can you pass me the sugar?
--- What's an appropriate answer? "Yes, I could. If you ask this question, you are not actually asking them if they will pass you the sugar. You are just asking, "is it possible for you to pass me the sugar?" So the answer, "yes of course, it's possible I could/can pass you the sugar."
(d) Would you pass me the sugar?
--- Now you are requesting an actual action. What's an appropriate answer? はい、どうぞ。
(e) Can I go to the bathroom? (I recall often a teacher correcting students when they asked for permission in this way.)
--- The teachers would say, "yes, it's possible for you to go, but you cannot go now."
(f) May I go to the bathroom? (This is a very specific question, asking for permission to use the bathroom at that exact moment.)
--- Then the teacher will either say yes or no, and it's a very specific answer. "Yes [you can go now]." OR "No [you cannot go now]."