The difference seems to be how you frame the concept. From Hopper and Traugott's book, some linguists believe that grammaticalisation could be understood as 'entering the grammar of a language', i.e. 'becoming grammatical', which assumes that 'grammar' is an fixed entity which things can enter and leave. Grammaticisation, by contrast, focuses on the lexical item being grammaticalised itself - it's the process whereby this lexical item becomes more and more narrow in distribution and the phrases containing it become more and more formulaic, and eventually the item acts as a functional word rather than a lexical one. H&T do not commit to this distinction, but are merely explaining the viewpoints of linguists who do differentiate between the .
