The word 'gravity' is more directly and restrictedly nounal than the word 'gravitation' is, in that 'gravitation' is the nounal form of the verb 'gravitate', while 'gravity' is derived directly from the Latin 'gravitas', a 3rd-declension noun related to 'gravis', which is an adjective that means heavy. We use 'gravitas' unaltered in English to mean something like seriousness, in a metaphorical application deriving from its meaning of weightiness.
The word 'gravitation' allows for suffixes that produce words of other 'parts of speech': 'al' yields the adjective 'gravitational', and appending 'ly' to 'gravitational' gives the adverb 'gravitationally'.
Some writers in English use 'gravity' to refer specifically to the Earth's gravity acting upon objects on Earth, and use 'gravitation' to refer to the associated force more generally. Other writers tend to use the words more or less interchangeably, with style being a consideration for which to use when. Science writers in general tend to use the adjective 'gravitational' and the adverb 'gravitationally' frequently enough, that for the noun form, they're in general more apt to use 'gravitation' than 'gravity', except perhaps when they're speaking informally.