Energy and matter are considered to be two different ideas, but they are actually very interrelated.
According to quantum physics, light is said to have properties of both energy and matter. It has diffraction patterns that appear when light goes through a slot, meaning that it has wave-like properties associated with energy, and light is also described as a stream of packets of light called photons, making it also seem to have particle-like properties.
It has also been shown that matter has wave-like properties as well. If you take a chemistry course, you will talk about how the electron can behave like a wave, and how it affects the properties of atoms.
Matter and energy can actually also be converted from one form to another (but not annihilated, as the Law of Conservation of Energy dictates). When you drive your car, gasoline undergoes a combustion reaction where it reacts with oxygen to produce water vapor and carbon dioxide. However, some of the mass is converted into mechanical energy, which powers your car. Energy can also be converted to matter as well, but this is rarely seen (only in particle accelerators, which is how positrons, the antimatter form of the electron, were discovered).
So in short, the answer is that matter and energy are different from one another enough to be thought of two separate ideas, but close enough to have connections to one another.
Speed and velocity are not considered to be matter. Both are defined as the change in position over time, with velocity also indicating direction as well. However, it takes a force to create motion, by Newton's 1st law, and it takes energy to create a force.
