A farmer is someone who owns and runs a farm. Farmers look after animals, plant big fields of crops and then harvest them, and generally do a lot of work starting very early in the day keeping everything on the farm running smoothly. Farmers usually live in the country a long way from the city so it can sometimes be lonely being a farmer.
A farrier is someone who looks after horse's feet. They fit horseshoes, and trim and balance horse's hoofs so they are at their healthiest. They can also fix horse's feet when they are damaged.