Two runs with the same prompt, the same seed and different samplers produce recognisably different images. The sampler is a real creative variable and it is usually left at whatever the interface defaulted to.
The trade-off is roughly speed against stability. Faster samplers converge in fewer steps and are more prone to changing character between runs; slower ones are steadier, which matters far more on a set than on a single frame.
Pick one, record it in the set specification, and do not change it mid-campaign. A sampler change halfway through a set is a drift source nobody will think to look for.
Does the sampler need to stay the same across a campaign?
Yes. Changing it mid-set introduces a difference that looks like model drift and is very hard to diagnose because nobody thinks to check it.
Which sampler is best?
The one that is stable across runs for your shot type. On a single hero frame, speed is worth trading for quality; on a hundred-shot set, consistency wins.