包 is bun (specifically a filled bun), and more generally denotes a package or bag, which the character resembles.
In Mandarin, 包 is suffixed with 子, which generally denotes small things or offspring (the character resembles a baby with its arms spread).
包 is also part of 打包 (dá bāau), which you say to indicate you want leftovers wrapped up to go.
Bao, a core component of classic dim sum, are wheat buns (mostly steamed, but some are baked or pan-fried), with various fillings (non-filled bao are called mantou, the original name for filled and non-filled bao and still used that way in some regions).