Student grades have fillers added and sometimes the pigments are not as pure as the professional grade. Some colors only come in the standard size from some manufacturers. It is usually most economical to use the standard size for most colors and the large for white. In oil painting white is a much used color that deserves its own discussion. In the case of oil paints, that binder is some sort of oil, usually linseed oil.
Oil is what makes the pigment fluid and, when it dries, it is what holds the pigment to the surface.
Drying oils Linseed Oil - An extraction from the seed of the flax plant, the same plant that is used to make linen for canvas. Excellent for use as grinding medium in oil paints. Due to its expense, it has been replaced by steam-pressed linseed oil in commercial manufacture of paints. Commonly used as a binder in tube oil paint, it is very transparant and will yellow to some extent. Equal parts of oil and water are mixed and exposed to the sun for a matter of weeks.