How do startups evolve when two create identical products (just out of coincidence) and both start taking off?

This is something that concerns me but maybe it's not as concerning as I thought. When you're focused on a product, and you launch, you want to be the first. This way you have a bigger splash and more people talk about you. However, in reality I'm sure there are situations where two products hit the market and pretty much do the same thing. I guess what you do in this situation is just really focus on the customer and try to carve out a niche? Like they do high end, low volume, and you do the reverse? Or you would focus on a certain demographic or user type? I don't ever think it would be a situation where one of the companies is obliterated. Unless you're really thick and refuse to pivot, even slightly.