These are two different families, with names that are actually pronounced a little differently in Japanese, and if we're being precise with transliterations, should be written differently: Mori (森) is the name of Ranmaru's family, and the Mōri (毛利) of Aki were the clan Hideyoshi was besieging at that point. The mark over the 'o' there is a macron, which means that it's a long 'o' rather than a short 'o'.

(There are a few factors that lead to confusion and irregularities in how we write Japanese historical names, especially in informal internet discussions. Macrons aren't easy to type. They need to be inserted. Older sources represented long o sounds with "ou" or "oo", depending on the word. Non-historical texts usually make no difference between short and long vowels. In general, macrons are the most correct, but it's a real pain to remember to put them in.)