Where these names come from
Words such as herd, flock, pack and school are in everyday use. Many of the more colourful ones, such as "a murder of crows" or "a parliament of owls", come from lists of hunting terms written in England in the 1400s, where inventing clever group names was something of a game. They have survived because they are fun.
Which should you use?
In an examination or a science report, the plain words are always correct: a herd of elephants, a flock of birds, a school of fish, a swarm of bees, a pack of wolves, a colony of ants. Keep the fancy ones for quizzes and stories. Some animals have more than one accepted group name, so answers in different books can differ.