Tested:
INSERT INTO dbo.CollegeDetails
(CollegeAutoID,CollegeCode,CollegeName,CollegeType,InstitutionType,Address,Pincode,Location,District,AffiliatedUniversity,EstablishedYear,IsActive,AddedBy,AddedOn,CollegeCategoryAutoID,WebAddress,CollegeNameID)
SELECT CollegeAutoID,CollegeCode,CollegeName,CollegeType,InstitutionType,Address,Pincode,Location,District,AffiliatedUniversity,EstablishedYear,IsActive,AddedBy,AddedOn,CollegeCategoryAutoID,WebAddress,CollegeNameID
from dbo.MedicalCollegesDetails