話し - This is a noun that means something like "a talk" or sometimes we'd translate it as "a story". When using it as a noun it's normally written just 話 but still pronounced "hanashi". In some types of verb conjugations though you will see 話し. 話す - This is the verb for "to speak". This form has a few different names but some of them are "casual form", or "dictionary form", or even "plain form". This is used when talking to friends and family. 話します - This is the exact same verb as 話す but instead of being in its plain form, this is the "polite form". This form also has a few different names (like "masu-form" because it ends in masu) but mostly is just called the polite form. This is used when talking to people you don't know very well, or people who are a little bit above you in status. Also you have my name. :P

話し means "Story" I think. But it's also the stem of hanasu. --> HanaSHIte imasu The others both mean to talk but you'd only use hanashimasu in a formal situation. I suck at explaining stuff so sorry.