Mixing ratio really has no units, because they cancel in the numerator and denominator of the fraction. It gives the ratio of a particular substance to the sum of all of the other substances (e.g., "1 part in 10 parts", where there is, say, 10 grams of "A" and 100 grams of everything else).

When the mixing ratio gets large, say 1 part A and 1 part everything else, we will say the mixing ratio is 1:1 but also call it 50%, which is the fraction 1/2. We make the change to "amount/amount of everything" for the percentage expression because we are looking at the fractional amount of the total rather than the ratio of one to others. This is more appropriate when the fractional amount is greater than about 25% or so.

Concentration has units that look like density (mass/volume), but it's not the same as bulk density. It depends inversely on volume, so one can take some gas molecules and throw them in a box of a known volume and calculate the concentration; but if we take those same molecules and throw them in a bigger box, the concentration will be less because the same number of molecules have to occupy a larger volume. It doesn't matter what else is in the box (other gas molecules, dead space, etc.), the concentration depends on how many molecules of the particular gas (or the mass of the gas molecules) are in the sample volume of gas(es), and the total volume of the sample.

Even though these two measurements are different from each other, there is a tendency for both to increase at the same rate as the amount of pollutant is mixed into a mixture. We will therefore use the term "concentration" to qualitatively refer to both mixing ratio and true concentration. For example, if the mixing ratio increased from 10 parts per million to 20 parts per million, we can say that "the concentration increased from 10 to 20 parts per million."