For me, intelligence is the processing of knowledge and wisdom is the application of knowledge (not as skill, because that's one way to understand it, but like connecting theory to real life).
It's hard to explain properly because it's abstract, but it can be imagined pretty simply by comparing to a neural network. An evolving network can process only a certain amount of input before it gets overwhelmed, and that's intelligence. How much you can process and understand. Wisdom is the evolution of the neural network; with time, the theory you learn is connected to more and more closely or loosely related things. The more connections there are, the better you can navigate around a subject and understand its diffeent aspects.
An example of this can be someone seeing fire for the first time. If they're intelligent, they'll be able to analyze how it interacts with the environment and deduce it's dangerous to the touch. Wisdom comes to those that understand a lot about fire, so they know it'll burn wood when it's kept in a flame for a while, and then it'll keep burning and give them heat. An intelligent person may infer this, but they don't know this.
Overall though intelligence and wisdom are connected very closely, and you probably wouldn't talk about one without the other. Trying to define them separately is bound to be inaccurate to some degree, like trying to explain the construction of a bridge without the ground to put it in. You can get pretty far, but you won't have the full picture.
