The physics definition is that matter has mass even when it is not moving, while energy only has anything when it is moving. We call this a "rest mass". So, for example, light is energy, not matter. It gets tricky when you talk about forms of energy that are made of moving matter such as sound, heat, or electricity - are they matter or not (the things doing the moving sure are)?

As a general rule, if it takes up space, it's probably matter. If it has mass even when it isn't moving, it's definitely matter.

Something that is matter will have mass. Some examples of things that exist but have no mass are energy (e.g. heat and light), magnetic fields, and electric fields.