C already has product types, so it's sums that are more interesting, and indeed the destructors for sums are harder in C. The constructors
in1 : a -> Sum a b
in2 : b -> Sum a b
sum : Sum a b -> (a -> c) -> (b -> c) -> c
There's a difference between "having a destructor" and having a first-class representation of it. For instance, basically every language has a destructor for booleans—it's just if.
The trick is that unless you have first-class functions you probably cannot reify such a destructor. It always just lives in your syntax.
On the flip side, that's really what it means for a language to, say, lack sum types. It's not that the language doesn't have the ability to have choice, it's that it lacks the ability to represent choice in data. In other words, you probably can eliminate choice using if/switch/case/what-have-you but you can't construct it.
Right. I interpreted your previous comment as meaning that you don't need pattern matching because you can just used the (reified) destructor. Conversely, you can avoid the higher-order destructor using pattern matching.
Yep! They are "the same".
More concretely, even without pattern matching, so long as, for instance, these three functions are all defined
You'll be equivalently expressive.