The Difference Between Density and Dimension

Density is a frequency within a dimension.

Third density and fourth density are frequency levels of physical reality, in what we call the fourth dimension - three of space and one of time.

Physical reality as an experience has different density levels in it.

Third density is a lower vibration of the fourth dimension.  Fourth density is a higher vibration in the fourth dimension, where many are now heading, ascending, leveling up their vibration, to become a more refined version of the physical experience in the fourth dimensional reality.

The fifth dimension is crossing into nonphysical reality.  So fifth density is the first density level in non-physical reality in the fifth dimension.  You can tap into the fifth dimension, and tapping into the energy of the fifth dimension can pull you up in the fourth dimension, so you can become a fourth density being in the fourth dimension.

As you may have started out as a third density being in physical reality, allowing yourself to tap into your higher/authentic mind, which is in a nonphysical reality, fifth density, fifth dimension - can allow you to raise your frequency to become a fourth density fourth dimensional being - a higher version of yourself in physical reality who’s more in alignment with the fifth density, fifth dimensional higher mind who exists in non-physical reality. 

So densities are like states within a country and dimensions are like a different country.