A label is generally a piece of paper or cloth that identifies a product and its maker. It is the medium on which the information is printed. As a verb, it refers to the act of placing a label on something.
You can always identify Saint Nick coffee by the red and green label on the tin, with the picture of Santa Claus in the upper left corner. It's the only coffee that looks like that!
Once I had made the hot sauce and let it cool, I bottled it. I had labelled the bottles the night before, so all that remained was to put them in the gift baskets I'd bought. I was sure my family would love my Roasted Garlic Madness Hot Sauce! Label can also refer to a short word or phrase that reductively describes a person or group.
Label can also be used in this sense as a verb, to describe the act of classifying or describing something in this way.
I got into a political argument with my father, and he called me a "bleeding heart." I was hurt by that label, since it makes it seem that my political view is all there is to me.
A brand is a logo or distinctive name that identifies a product as being made by a particular maker. Levis is a brand of jeans. Apple is a brand of computer. Brand can also refer to the act of marking something by burning a mark, graphic, or words into something, and also the mark itself.
My wife's favourite brand of chocolate is Ritter Sport. She would rather not have chocolate than eat any other kind, especially the praline variety. I must admit that I agree with her.
The practice of branding cattle continues in the twenty-first century, even though animal rights organizations routinely protest against it. Cattle ranchers say it doesn't hurt the cows, but there are many who disagree.
If you want to say that something is entirely new and just created, you would say it is brand new. For extra emphasis on the newness, you might say brand spanking new.
I feel bad for Tommy. Here he is, on his first day with his brand new car, and he gets into an accident on the way to work. The car is totaled.
You can spot an amateur fisherman a mile away. Just look for the person who seems tentative and has a brand spanking new fishing rod and reel.