the difference is the following:
تبديل means to kind of change but its more like replace something, so for example when you change your Cloth, you're actually replacing your cloth with other cloth, so here you use تبديل
أغير: means simply change
but you have to know that those both words are mostly used for the same thing and replace each othher in sentences, so to make it short people don't really differentiate between those two words.
some people would use أغير for changing cloth. so it's no big deal :)
قمت بتبديل ملابسي (qumtu bitabdil malabisi)
I changed my cloth.
قمت بتغيير رقمي. ( qumtu bitaghyir raqami)
I changed my number
قمت بتبديل القميص اللذي اشتريته في المتجر ( qumtu bitabdil alqamis al-lathi shtaraituhu fi-lmatjar .)
I changed the shirt that I bought (for another) at the store .
hope I could help :)