An atom is composed of a nucleus, containing protons and neutrons, around which there are electrons. The number of protons determines what element this atom is (one proton, it's hydrogen, 6 protons it's carbon, 92 protons it's uranium...)

Plasma is a state of matter, like gas, liquid and solid. It is composed of elements. Plasma is matter that is so hot that the electrons are not bounded to atoms anymore and start moving around. But the atoms are still there, they've just become ions (atoms which have lost electrons). For example, the Sun is made up of a plasma of mainly hydrogen and helium, with some other trace elements.

The vast majority of observable matter in the universe is in the stars. The Sun makes up 99.85 % of the mass in our Solar System. So yes, the observable matter is nearly all in a plasma state, and is mainly composed of hydrogen and helium.

Now you may start to wonder why I talk about "observable matter". Well, because there may actually exist another type of matter, called dark matter, that has been hypothesized to explain why galaxies are heavier than they seem to be. This dark matter may be more than 5 times more abundant in the Universe than common matter, but we haven't observed it yet.

In the observable Universe, there are also things that are not elements.

First, elementary particles : electrons, protons or neutrons not in an atom, photons (particles of light) and other more exotic particles like muons or neutrinos. These are things smaller than atoms. Particles don't stick together to form bigger things like atoms do (except protons, neutrons and electrons that make up atoms), so you can't have something visible made of muons.

Second, matter that have been crushed so much that in the atoms, electrons and protons have fused together to make up neutrons. This requires an enormous gravity and is only happening in really massive stars when they die : they form what is called a neutron star.

And finally, black holes. Matter crushed so much by gravity than it's not even matter anymore. It's just a point with an enormous mass.

Plasma just means the substance is mostly charged particles rather than being mostly neutral. In practice, this means a lot of hydrogen and helium nuclei that have been separated from their electrons. We know where it is on the periodic table, it's just ionized.

This isn't too surprising. Most of the matter in the universe is in stars or dispersed in near vacuum, both of which are conducive to plasma formation.

Also, this means 99% of the visible ordinary matter in the universe.