The two numbers connect through a subtraction. Take the gross rent for the unit, which is the rent plus a utility allowance if the tenant pays some utilities directly. The housing authority calculates the tenant's share, roughly 30 percent of their adjusted monthly income, and pays you the difference between that share and the gross rent, capped by the payment standard. That difference is the housing assistance payment, and it lands in your account by direct deposit.
So with round numbers. Say the payment standard for a two bedroom is 1,400 and you're approved at 1,400 gross rent. Tenant's adjusted income works out so their share is 300. The authority pays you 1,100, the tenant pays you 300, and you collect 1,400 in total. If that same tenant's income goes up at recertification and their share becomes 450, the authority drops to 950. Your 1,400 doesn't change. The split inside it does.
Nobody eats a gap in that example because the rent was set at or under the payment standard. A gap appears if you ask more than the standard. Then the tenant would have to cover the excess out of pocket, and there are limits on how much of their income the authority will let them commit, which is why an over-standard rent often just gets rejected instead. Confirm the local rule with the authority in writing, because payment standards and how strictly the excess is allowed vary by housing authority.
The piece that matters to you as a passive holder is that the tenant portion is not guaranteed. That 300 is a normal collection problem with a normal eviction process behind it. What's dependable is the 1,100.