"أريد " is a formal word , it's used in formal arabic language and i think it's also used in UAE and Gulf, while "بدي " is a colloquial word used in Syria , Lebanon , Jordan .. but their meaning is exactly the same.

you are right! they both mean " want " but "اريد" used mainly in standard Arabic and also used in some dialects (colloquial). while the word "بدي" is used as a colloquial word in some dialects such as Lebanon. Here in Egypt we use the word " عايزة/عايز" to give the same meaning.

Exactly, Same meaning but simply two diffrent types of Arabic أريد pronounced as Oredo that's MSA (modern standard Arabic) بدى is shami or lavent both means the same which is I want.

Simply ... بدي Beddi is dialect .. أريدُ Urydu is Standard Arabic .. if you come to Algeria for example and say BEDDI it will be strange and a lot will not understand .

بدي suggests the meaning of "I would like".