Pigtails are smaller and thinner and resemble pig tails. Bunches hold a lot more hair and don't resemble pig tails. Crazy hey!

Pigtails usually means "two small, basic braids, resembling the tail of a pig", although many native English speakers mistakenly refer to "ponytails" or "twintails" as pigtails. (In case you ask, ponytails/twintails are two small, basic ponytails. You might imagine Hatsune Miku, who wears ponytails very high up on her head.) A famous character with pigtails is Pippi Longstockings. The word "bunches" is a little bit vague, because it literally means "hair gathered into two or more clusters or piles" (the word bunch is used for many things, like "bunches of oats", little clumps made of oats stuck together and dried. Or, "a bunch of hay", meaning a haystack or hay pile of any size or shape.) But usually, when someone says, "I put my hair in bunches", they mean, "I put my hair in ponytails". Bunches are often more loosely gathered, stylish, and curly than ponytails. If you meet a young person who does not know this word, they may not have spent a lot of time around elders, or reading older literature. They are also probably a male. . . . Many males do not know all the words to describe different hairstyles, haha! :) Best wishes. Keep working hard! You are doing great!

For one thing, I've never heard of bunches. (Native US speaker here.) It looks to me like they mean the same thing but each of those words is used in different regions. For example, as a person from the US, I have heard of pigtails but I had never even heard of "bunches" in the context of someone's hair before this very question you are asking.