Firstly, we don't use 여러가지 for people. For example, 여러가지 사람 is rude expression. it sounds like racism or something like that. but we use 여러 for either 사람 or 물건 여러 사람 means 'many people' 여러 나라 means 'many countries' 여러모로 means 'in various ways' 여러 영화 means 'many movies' etc and 여러가지 include types of things For example , 여러가지 컴퓨터 means 'various types of computer.' 여러가지 운동 means 'various type of sports.'

Thank you!

여러: various/many 여러가지: various/many kinds of