They're not the same. Lots of lexical differences between Taiwanese Minnan and the varieties spoken elsewhere (such as by the Straits Chinese, i.e. those who primarily call their language "Hokkien" I think). In particular, numerous Japanese loanwords absent from other flavors of Minnan, such as 中古 or 便當 (the latter also happens to be part of your username). For the most part, the languages have been developing independently for centuries. So, shortening "Taiwanese Minnan/Hokkien" to "Taiwanese" is more accurate than calling it just "Minnan" or "Hokkien" in my opinion. And it's also what the language users themselves seem to commonly call it.