One of the main differences in reasoning I think is how each paradigm deals with time, not in a datetime or library sense, but in the literal sense of time and causality. Does the paradigm abstract the passage of time or not? FP abstracts away time, and statements in FP are timeless, true now and in the future. That is why it ends up looking like math a bit more. Once statements in the language are sensitive to time... that means there is mutation and the line above can have a side effect on lines of code below. It's like FP is jumping a dimension and it makes statements that have to be true at all times (pure FP anyway), while mutation languages give you fine-grain control on what is being computed each unit of time.
Of course you then have a mixture of both, which many if not most modern languages have. Pure FP can be expressed in a language that supports mutation anyway, it's just a matter of how much first class support those features have. Languages like Haskell I think go so far into the abstracting of time, that they reached around and achieve something like mutation based syntax, except there is a tower of abstractions working under the hood, ensuring that it's still timeless equations which result in side effects.
Of course you then have a mixture of both, which many if not most modern languages have. Pure FP can be expressed in a language that supports mutation anyway, it's just a matter of how much first class support those features have. Languages like Haskell I think go so far into the abstracting of time, that they reached around and achieve something like mutation based syntax, except there is a tower of abstractions working under the hood, ensuring that it's still timeless equations which result in side effects.