The measure is a ratio, and the arithmetic is worth understanding before the label is. Months' supply is the number of homes for sale divided by the number selling per month, so it answers a single question: at the pace things are currently selling, how long would it take to sell everything now listed if nothing new were listed. The Census Bureau and the Department of Housing and Urban Development publish it every month for new houses in their joint New Residential Sales release, where it is reported in exactly that form, as a supply of so many months at the current sales rate.
What the agencies publishing it do not do is label it. The release states the figure, states how it changed against the prior month and the prior year, and stops. It does not say that any particular number makes a market favor buyers or sellers. That absence is the most useful thing to know about the labels, because it means the familiar dividing line came from somewhere else. Sources that do quote a threshold do not agree on it: some describe roughly six months as balance, others put the boundary at four, and none of them is applying a standard set by whoever produced the underlying data. So a source telling you a market has crossed into one category is reporting its own convention, and it is worth asking which one.
The denominator moves, and that is where most confusion about "inventory" comes from. A market can move toward buyers in two entirely different ways. More homes can come up for sale, which is the picture the phrase suggests. Or the same number of homes can take much longer to sell because buyers stepped back, often because borrowing became more expensive. The second route produces a rising supply figure with no increase in the number of houses at all, and it does not feel to a seller like an inventory problem. Reading the ratio without asking which of its two parts moved will mislead you about what is actually happening.
The label hides the fact that price is only one of the things being negotiated. In a market tilted toward sellers, competition shows up first in things that are not the price: how quickly a buyer will close, whether they will accept the property as it is, whether they will pay their own costs, how few conditions they attach. In a market tilted toward buyers, sellers give ground in the same currencies before they cut the asking figure, contributing toward the buyer's closing costs or paying to reduce their interest rate for a period. Two identical sale prices in the two conditions are not the same transaction, which is why the reported price alone is a poor guide to who had the upper hand.
Neither label is national in any useful sense. Housing is a collection of local markets that can move in different directions at once, and within one metropolitan area the conditions for a starter home and for a large house at the top of the local range are frequently opposite. A national statistic is genuinely informative about the national picture and tells an individual buyer or seller very little about the twelve homes they are actually choosing between. The figures that speak to a specific decision are local and recent: how long comparable homes are taking to sell, how many are reducing their asking price, and how many are closing above what they asked.
The condition is a snapshot, and it is not a forecast. Both labels describe where things stand, usually with a reporting lag of weeks, and neither carries any information about how long the balance will last. A market can shift within a single season when borrowing costs move, because the cost of the monthly payment changes what a given buyer can bid without anything about the houses changing at all.