The VP of R&D is responsible for taking ideas and making products.
The CTO's job is to lay out the technology strategy so that the VP of R&D can develop plans to realize the vision.
They can sometimes be the same position but that's rare. Usually, a startup will either have a VP of Engineering (R&D) or CTO -- having both can be overkill but does happen, especially if the technical founder needs help in implementing.
Jarie's spot on. To build off of that, it's also a question of scope and role - really, it's based on how deep an organization can / needs to be.
At a small company or a startup, as he mentioned, these roles overlap / are a single person.
At a large corporation, the CTO is responsible for communicating and executing the big picture tech strategy. That means is taking input from the executive team (CEO, COO, CMO, CSO) as well as giving the technical perspective in those discussions. From there, the VP of R&D is responsible for actually acting on the strategy - e.g., CTO says "we want our customers to use our product in the cloud," and the VP of R&D is responsible for creating the products and initiatives to make that happen.