There's a big difference between cancel culture and boycotting. Cancel culture is active, boycotting is passive.
In cancel culture it isn't sufficient to just not patronize a business. Instead, with cancel culture participants actively seek ways to attack and destroy the object of their outrage. Boycotting is the simple act of not patronizing a business or activity because you disagree with them.
So, in a cancel culture, you see things like a bakery not wanting to make gay wedding cakes attacked and sued out of business. J K Rowling, among other artists and authors, saw the same thing. It wasn't enough for those offended by her comments to simply not buy her books, they actively sought to get her removed from all social media, get her publisher(s) to drop her as a client, have her books legally banned from sales, etc. That's cancel cultue.
A boycott is the simple act of not patronizing a business, service, or activity. I disagree with your position, so I won't patronize your business. It doesn't involve actively seeking to keep others from patronizing that business by force if necessary. It doesn't involve active attacks on that business online or off like cancel culture does.