I'm wondering, is a cat smarter than a dog? I mean if you train the dog maybe. But without training?

Well, you have to be a bit more specific. Dog brains among breeds vary in size and capability. Dogs have roughly the same intelligence as raccoons and lions. Meanwhile, the average house cat compares to a bear in intelligence. All in all, some dogs are more intelligent than cats. However, I used to have a cat that could literally communicate through hand gestures and understand us, so it doesn't apply to every dog or every cat.