They look near enough identical, which makes the price gap puzzling. Cutting one open explains it immediately.
Same outside, different inside
Burrata is a pouch of mozzarella filled with torn mozzarella and fresh cream. The shell tastes exactly like mozzarella; the inside is closer to cream, which is why it spills when you cut it. It began as a thrifty way to use up offcuts from mozzarella making, and now sells for considerably more. Shell and filling in the same mouthful is the whole point of the cheese.
The same skin, a different centre:
The filling has a name: stracciatella
What fills a burrata is called stracciatella — mozzarella curd, stretched in hot water and then torn by hand into fresh cream. That is why you can feel threads in the cream rather than a smooth emulsion. Uneven is correct here, and in fact a sign of a good one. Stracciatella is now sold on its own in tubs as well, which is simply a burrata's filling without the pouch.
They are handled completely differently
Mozzarella is an ingredient; burrata is closer to a finished dish. Heat splits burrata's cream, so do not cook it. And it wants eating the day you buy it — the window is ten to twelve days from making, and even a day can soften the cream and toughen the shell. Deciding when you will eat it and buying for that day is the single best way to buy this cheese. Mozzarella is far more forgiving.
Cow's milk and buffalo mozzarella
Mozzarella divides within its own name too. Buffalo milk carries nearly twice the fat of cow's milk, so mozzarella di bufala is markedly creamier and more aromatic — and several times the price. The word bufala on the pack is what tells you. To eat as it is, buffalo is clearly better; for pizza, cow's-milk fior di latte is the sounder choice, since buffalo mozzarella carries enough water to leave the base soggy unless you drain it first.
Which to buy
Burrata if it is the centre of a salad or going out as it is; mozzarella if it is going into something. Fresh mozzarella is sold sitting in liquid — choose one where the liquid is clear and the ball is smooth. The shredded bags sold for pizza are a drier, different product, and some of them are processed cheese, so the ingredients list is worth a glance. With burrata, check the date before you check the price.