【Change】 , 【alter】 , 【vary】 , 【modify】 (and their corresponding nouns 【change】 , alteration, variation, modification) are comparable when denoting to make or become different (or when denoting a difference effected).

【Change】  and 【alter】 are sometimes interchangeable; thus, conditions may 【change】 (or 【alter】 ) for the better.

【Change】 , however, usually implies either an essential difference, even a loss of identity, or the substitution of one thing for another while 【alter】 stresses difference in some particular respect (as in form or detail) without implying loss of identity.

【Vary】 frequently implies a difference or a series of differences due to 【change】 (as by shifting, diversification, or growth).

Sometimes it implies a deviation from the normal, the conventional, or the usual.

【Modify】 suggests a difference that limits or restricts; thus, an adjective is said to 【modify】  a noun because it definitely reduces the range of application of that noun (as old in "old men" and red in "a red rose"). Often the word implies moderation (as of severity) or toning down (as of excess).

【Modify】 may sometimes suggest minor changes or absence of radical changes.