Datacenter proxy is the proxy server assigned with a Datacenter IP. Data center IPs are IPs owned by companies such as AWS( Amazon Web Services), Azure Cloud, Digital Ocean, Linode.
Residential proxies are proxy servers assigned with residential IPs. These are IP addresses that are assigned to users by an ISPs. ISP being that company that you have to pay for your home internet connection, the companies like Verizon, AT&T, Comcast, Spectrum, Cox, Time Warner and so on.