I agree with the first one, but age is measured in days at a minimum, so twins are always the same age. (I'm sure there are cases where they are born farther apart due to some issue with the pregnancy, but that is statistically insignificant here.)

Even if you take days, one can be born at 23:58 and the other at 00:03 the next day. (And it could be New Year’s day — in some cultures that would even imply different ages in years.) Regardless of days, it’s not uncommon to talk about who is the older twin.

Of course colloquially twins are the same age, but we are talking about a mathematical puzzle about probabilities here, where precision is paramount.