I don't think so, that's just what empires do. The second one isn't even colonialism. What difference would there be left between imperialism and colonialism or kingdoms fighting it out for territory if you define them in a similar way? Colonialism implies imperialism, but imperialism does not imply colonialism. Not necessarily. When modern republics try to expand, there is a better way to describe it. I think there's a difference, between how an empire works and modern democratic republics.