The first snippet you wrote makes sense for string, but not for vector. For vector, you'd need to do:

   if (x_Vec.find(another_x) != x_Vec.end()) {
      //some code
   }

The reason why vector doesn't have contains() is because it would be an O(N) operation for a vector. STL is generally designed in such a way that, when something needs to do an O(N) lookup, it has to deal with iterators, making the iteration happening in the background a bit more explicit.

But, for example, for std::set and map, you can just do:

   if (a_set.count(x)) { ... }

It's not a good pattern for multiset and multimap, since it won't stop at the first occurrence. C++20 finally added contains() for that reason - but, again, only to associative containers.