Can I Replace My Hardwired Smoke Detectors with a Different Brand?

I'm looking to upgrade my home's hardwired smoke detectors. There are currently three interconnected units, and I'm tired of the kitchen one going off every time I cook. I purchased some new detectors, but the connectors don't match. I'm wondering, do these interconnected smoke detectors all run through a single wire? Is it possible to replace all three with a different brand without any issues? I thought it would just be a matter of rewiring them with the same connections, but I'm not sure if that's the right approach.