Car vibrations

I have two seemingly separate vibration issues with the car listed above Ex model. First, when the car is maintaining speed with foot on pedal (more noticeable at higher speeds and up hill) there is a consistent vibration that goes away when off the pedal or when accelerating quickly. Second, when at a stop in drive with foot on brake I notice a "hard" or "deep" vibration not violent. I am wondering if these really are two separate issues or if they are caused by the same thing. Other than those instances no other vibrations felt. Any help in figuring this out would be much appreciated. Please do not hesitate to ask questions. Thank you.