"Eat like a horse" and "Eat like a pig" are both idiomatic expressions that describe someone's eating habits, but they convey different meanings and connotations.
"Eat like a horse" suggests that a person consumes a large amount of food. This phrase implies a hearty appetite and can be used to describe someone who eats more than the average person. The comparison to a horse emphasizes the quantity of food being consumed.
For example, if someone says, "My brother eats like a horse," it means that he has a voracious appetite and can consume large portions of food in one sitting.

"Eat like a pig" implies a lack of manners or restraint while eating. This phrase suggests that a person eats messily, noisily, or without regard for etiquette. It emphasizes the way in which the person eats rather than the quantity of food consumed.

For instance, if someone comments, "Look at that child, eating like a pig," they are referring to the child's messy and uncontrolled eating behavior.

In summary, "eat like a horse" focuses on the quantity of food consumed, indicating a large appetite, while "eat like a pig" emphasizes the manner or behavior of eating, implying a lack of manners or restraint.