Well yes, אישה is an example of excessive spelling, where more Juds and Waws than than in the usual spelling are used, but I suppose this spelling is gaining ground, because the original reason, the doubling of the Shin, which made its first syllable originally closed, (אִשָּׁה [ish-sha]), is not felt any more, because the etymological false derivation from אִישׁ is so suggestive.
Parents in America often use the word “lady” when speaking to children because it’s easier for them to understand than “woman”, and other people use the word “lady” because it’s thought to be more polite than “woman”. Traditionally though, a lady was an adult female of some refinement or one who had a certain level of social status, whereas a woman was not at such a high social level. These days, a (perhaps?) old-fashioned mom might tell her daughter “A lady doesn’t use language like that.” This statement has a different nuance than “A woman doesn’t use language like that.”