Bull market
A sustained rise in market prices. The common convention dates one from a low point once prices have gained 20 percent or more, though no official body sets that threshold.
A bull market is the market's own name for a long upward run, and the 20 percent rule of thumb exists to separate a real run from ordinary week-to-week noise. The label is attached to a stretch of price history, normally running from the low that ended the previous decline up to the peak that ends the rise. The name is usually explained by the animal that attacks by throwing its horns upward, though the etymology is not settled.
It is a description written afterwards. Nothing marks the bottom at the time, and the low a bull market is dated from can only be identified months later, once prices have already climbed. Different publications also use different rules, some measuring closing prices and some intraday, some requiring the previous high to be passed before the run counts, so the same period is dated differently in different places. Treat any specific start date as one house style rather than a fact.
The mistake is reading the label as a forecast. Saying a market is in a bull run states only what prices have already done, and the convention carries no information about how much further the run goes. Past runs have ended from every level of confidence, including the highest. Its mirror image is a bear market, and most long price histories are made of the two alternating.