So there are several types of badger brushes and as a rule of thumb they differ In the quantity of the hair and the knot (all the hairs glued together to make the brushy part of the brush)…….now most brushes nowadays are just fine for every day shaving, as a rule of thumb) the quality goes as follows (lower cost to higher cost): mixed badger, pure badger, best badger, silver tip badger, super badger. People generally rank quality in the softness and water retention of a brush. These are generally brown in color and can have varying shades of brown from the stem to tip.
Boar brushes tend to be less expensive as compared to badger brushes. They are more firm than badgers and as time goes on, and more usage, the hairs get split ends - which is a good thing in this case. Boars absorb less water but are better if you have thicker whiskers to exfoliate. There are other benefits -so I am generalizing. In colors, these are usually blonde hairs - but they can be dyed to look like badgers.
Synthetic brushes - there are too many kinds to name and no real rules to naming them - are, again as a rule of thumb, in the middle between badgers and boards - they are usually more firm than badges, but retain their softness, and they don’t retain water similar to a boar. They come in any color of the rainbow so to speak. If your brush is gray - it is more than likely a synthetic brush. Some vendors call this gray to black a Timberwolf knot.
Badger
Boar
Synthetic:
As a rule of thumb - does it look and feel like real hair - then it is more likely a badger or boar. Synthetics, though soft, are plastic.
If it is firm and bristly and blonde /yellow- more than likely it is a boar. If it is softer and brown - it is more than likely a badger