"Within the month" vs "Within a month" is there a difference?

Just applied for a job and they said "Must be available to start within the month".

Does that mean by the end of month? In this case August 30th? Or does it mean 30 days from now, meaning September 17th? And would this be different from "within a month"?

Solution 1:

To my ears "within the month" means during the current month, that is by the end of August. "Within a month" gives you a full month from now, so if it is the 17th August today, you must start by 17th September.

It is a completely different question as to what the potential employer thought they meant: people are not always as precise as the language they use; it is best to ask for clarification.