Following, modified following, preceding — the market's names for how a date rolls.
In financial contracts the roll rule has standard names. FOLLOWING moves a date to the next business day. PRECEDING moves it to the previous one. MODIFIED FOLLOWING moves it forward unless that would cross into the next month, in which case it moves back.
Modified following exists because a payment schedule should not drift between months: a monthly obligation that rolled from 31 August to 1 September would land two payments in one month and none in another.
The convention is named in the contract and is not a default. Two otherwise identical instruments with different conventions produce different cash flow dates, and the difference compounds across a schedule.
The same mechanism. Business day convention is the market's vocabulary for it, with named variants a contract can reference.
One decides which DAY a payment falls on. The other decides how much interest accrued between two days. Unrelated problems, similar names.
See also roll convention · day count convention · business day · settlement date
We hold this as not held — the corpus records closures, not contract terms. See what we hold.