同一 (tóng yī) is a formal, attributive adjective meaning 'the same' — it always directly modifies a noun or classifier (同一本书 'the same book'). It is more precise and written than 一样 (yī yàng), which is used predicatively (这本书和那本一样 'this book is the same as that one') and in comparisons. 同样 (tóng yàng) is similar but often means 'equally' or 'likewise' as an adverb.