If the date is May 31st, and someone tells you about an event happening in exactly one month, what date are they referring to?

It seems generally accepted that May 15th and June 15th are one month apart. But what happens when the following month does not have a date matching the current date?

June does not have a 31st day! Is it possible that a month from May 31st would actually be July 1st, skipping the month of June entirely?

Discuss.