A botnet implies a level of control over the compromised device, normally achieved through exploits. A residential proxy is done through taking advantage of technically naive users, rather than exploits (proxyware, sort of like spyware/adaware) and doesn't aim to give control over the target device just over their internet connection. Botnets are run by individuals/hacking groups, and residential proxies are provided by "legitimate" businesses. In theory, they can both be used for the same purpose of DDOSing a target, but as most residential proxy resellers try and position themselves as legitimate, they are less likely to support a client that is using their service to DDOS people