If a person vows to fast for a month but speaks in general terms, the fuqaha’ say that he has the choice between either fasting for a month based on sighting of the new moon, in which case it must be consecutive days, and it is acceptable if the month turns out to be twenty-nine days, because this is still called a month; or of fasting for a number of days that is not connected to the lunar month, in which case he has to fast for thirty days, because if he fasts on the basis of the number of days it has to be thirty, and it is permissible for him to fast them separately. 

So he has the choice between fasting for a lunar month, in which case it is the month that counts, but it is also permissible for him to fast the number of days, in which case he must fast for thirty days, whether they are separate or consecutive.