I would like to know when to use 同一 and when to use 一样 when describing items or people as similar? What is the difference in usage between these two phrases?
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Note there are some (idiomatic) exceptions to these rules, which can be another topic.
Since you've mentioned 'similar', neither of these two words means 'similar'. You may want to use
A little digression: adding to the complexity is the phrase “同样” So, I think the first step to distinguishing between 同一 , 同样, and 一样 would be breaking them down into characters.
meaning of '样' is “appearance, kind, type, sample”. as user58955 mentioned, things with the same appearance/kind/type/sample do not have to be the identical thing. (However, "同一" may not even point to the same "instance" of an object, see example 2 below)
“一” and “同” may both mean "same" or "similar". But "一" implies a constraint on number: there is only one same thing in question.
More examples that may be interesting and are harder to generalize:
同一 is usually used to modify nouns to mean exactly the same object, as
一样 usually does not mean exactly the same object, we do not say 一样房间 to mean 'the same room'. It means, from the wording (一+样), both things look the same (but they are different objects). For instance,
同一 is a bit stronger than 一样.
同一 means the same thing. 一样 means the same kind (of thing).