Both help you organize your links, but they work differently. A Channel is simply a labeled group: you can tag any mix of links, bio pages, and QR codes with a color-coded channel to keep related items together, with the option to "star" important ones.
A Campaign is more than a label: it's its own shareable link with a rotator, meaning it can redirect to different destinations (useful for A/B testing a marketing push) and comes with its own combined statistics across everything inside it.