First off, its internal & external ip. External ip in lay man terms its public ip.
As long all devices are using the same router, all devices have the same external ip. Internal ip given by the router does not do anything.
When Jagex bans an external ip, all accounts having the same external ip, be it different devices has a slight chance to be banned (Chain ban). Thus it is advisable to get a proxy to prevent such cases from happening.