There are male and female forms. The difference becomes apparent in autumn. Female forms will produce berries (and they contain seeds) whereas male forms of bay trees do not generally produce berries.

So is the one with white balls going to develop berries? Is that a female one?

when the flowers open look for the male parts, like little drumsticks sticking up with pollen on them.

The female flower will have a central part possibly with a feathery or sticky tip. So the buds could be either. Though my culinary Bay has never flowered.

I've had my bay tree for rover 20 years and it has never flowered at all.