“看样子”多为从表面上、直观上的判断。多用于具体事物和口语，例：这桌子看样子比较结实。 “看起来”既可以用于分析后的判断，也可以用于从表面上的判断。例：这事看起来很容易，其实很难办。

I can tell you, most of Chinese people use "看起来” & “看样子” as a same word. So never mind in oral Chinese.

看样子 看起来 看上去 are the same.

The same meaning

It is like you are asking the difference between "it seems like" and " looks the same"