相同(xiāng tóng) - identical, the same, alike in Mandarin

相同 means identical, and it is the written or careful register. It is what you want for specifications, results, colours, conditions and rules: 相同的条件 (the same conditions), 完全相同 (exactly identical).

In speech, 一样 does the same job and sounds far more natural: 我们的想法一样 rather than 相同. A rough guide is that 一样 fits a conversation and 相同 fits a report.

The grammar differs too, and this is where learners slip. 一样 uses the 跟 A 一样 frame (这本书跟那本一样), while 相同 usually takes 和 or 与 plus 相同 at the end (结果与上次相同), or sits before a noun with 的. Note also the built-in opposite, 不同, which is a word in its own right rather than a negation you assemble.