I raised goats for many years. Most people who do that are interested primarily in production of milk.
They need to bear young every year in order to lactate, so you have to get your does bred. You either take them to someone with a buck, or borrow a buck (usually for a fee, or a couple sacks of feed) for the purpose.
This is a down-to-earth and not very scientific meaning of the word breed. As husbandry becomes more complex, breeding involves detailed records of breeding lines, and choosing a buck on the basis of his particular breed and whether it is strong in the characteristics you're after-- Saanens for example are known to be heavy milk producers, but don't do as well in hot dry climates as Nubians.
Breeding entails a certain amount of laboratory work nowadays, and is done largely, in many cases (prime cattle, racehorses) by purchase of frozen sperm and artificial insemination.
Raising is still the general all-encompassing term, but just as raising livestock requires complex dietary strategies, including supplements and inoculation-- decisions about breeding are made with each new generation, for the purpose of enhancing certain traits.
I still raise chickens with the strategy of cross-breeding certain roosters with certain hens, my goal being to create a new breed whose hackles (neck feathers) are barred (striped like a Plymouth Rock's) but colored in yellow and black instead of white and black.
The idea is to produce a feather that fly-tiers can wind around a hook to produce a pattern that looks like the segmented yellow abdomen of a bee or hornet.
Breeding entails manipulation, and much of it occurs in the research lab or benefits from discoveries made there. Raising animals is all about their care and cultivation, the production of bigger populations, and the chores involved-- pulling lambs (aiding in their birth), feeding and sheltering, docking tails and horns, shearing them and butchering them for market.
Breeding is a part of raising animals, just as feeding them is.