1) Baryonic
This is the kind of matter you are familiar with. It is made up of
neutron, protons, electrons. We are a sort of dark matter, so are cold
rocks floating out in space, since we all emit very little detectable light.
Other examples: planets, brown dwarfs and compact objects (like black holes),
However, we have a pretty good idea of how
much baryonic matter there is in the universe (from the fusion reactions
which occurred during the big bang). Baryons account for only 5% of the
critical mass in the universe, though we only 'see' about 10% of that.
So there is significant "dark baryonic matter". One form of baryonic
dark matter is commonly referred to as MACHOs (massive compact
halo objects). Astronomical searches in our halo have found MACHOs, but
there are not enough to account for all the dark baryonic matter.
2) Nonbaryonic matter
This you are not familiar with. In fact, no one is. All we really know
is it exerts its gravitational influence on normal (baryonic) matter,
but otherwise it doesn't interact (or very very little) with normal
matter.
Formation of Galaxies and Dark Matter
At the time of recombination, we see a fairly smooth distribution of
baryonic matter. Dark matter has acted upon that smooth distribution
to make it clump and form the galaxies and clusters of galaxies we see
today in a relatively short time period.
So, dark matter is actually needed in order to explain the formation of galaxies and galaxy clusters so quickly in our universe. For this reason, Cold Dark Matter, material that moves slowly and can help to clump up ordinary matter, is preferred over forms of dark matter called Hot Dark Matter, which moves very quickly and would not help to create the galaxy structures we see today.
How much dark matter is needed?
Interestingly enough, we do not need to have all the energy in matter
(dark or light, baryonic or nonbaryonic) to keep the universe flat. We only
need about 30% of the critical density in matter.
There is another source of 'energy' which can keep the universe from
expanding for ever, and which accounts for the other 70% of the critical
density. More on that soon.