The correct terminology is indeed
declension, which refers to the variant inflectional realizations of a word. In most cases, like Latin, declension means the set of alternative forms a word can take depending on its grammatical function (subject, object, etc), or the class of words that show the same alternations (1st declension, 2nd declension, etc).
Glenn said:
I think Japanese is highly inflected. Its adjectives, verbs, and copula all inflect for a variety of functions. You can think of the case particles in Japanese as being like inflections for the purpose of understaning declensions. For example, watashi ga has a different grammatical funtion than watashi ni, just like in English "I" shows nominative case, "me" shows objective case, and "my" shows genetive case (although these distinctions seem to be disappearing). That's basically how the inflections work, although there are different classes of declension just like there are different classes of verbs (like -ir, -ar, and -er in Spanish).
In Japanese, the variations of verbs and adjectives could be called "inflection", and the system of case markers "declension" in the broad sense, but, as lexico said, this is rather
agglutination, which is a bit different from inflection.
For example, nouns in inflecting languages can only appear in an inflected form, the stem of the word cannot be used alone. But in Japanese
watashi is a correct form, and you just add a particle. But in Latin the stem ros- of rosa, rosae, rosis, etc is not a correct form. In agglutination, you can draw a clear limit between an independant noun and the case marker.
Also, in agglutinative formations, each word is made of a string of morphemes which are clearly divisible, and each morpheme correspond to one meaning/function, while this is not the case with inflection.
For example, the English word "their" cannot be divided while it bears the meanings 3rd person pronoun+plural+possesive : all these elements are fused into the word. In Japanese, the equivalent "karerano" can be divided : kare 3rd person pronoun + ra plural + no possesive. This is the same thing with verbs : in Latin the indivisible form "amo" is simultaneously first person+singular+indicative+active+present. In Japanese forms like tabesaserareta are always segmentable : tabe + sase causative + rare passive + ta accomplished.