generally speaking, capacity can mean two things: (1) the ability （有沒有能力做這種產品） or the amount you can deliver (產量）。
capability means ability (usually, an ability to do a certain thing)..
so perhaps, we could say:
production capacity = 生產能力
production capability = 產能
but I'm not sure what the proper meanings of the business terms are, I can only answer according to the meaning of the english words.
and even then, these two terms can mean the same thing, but capacity usually does imply amount per time period (e.g.: how many per month)
but you could still say, "They do not have the capability to make so many units in such a short time", in this case, we are talking about their production capacity, but since they don't have the ability to make this production fast enough, we can also say their capability is not enough. (although they do have the capability to make the product. just not fast enough)