You are correct, wireless just means the network connection the camera still needs power run to it. I placed mine where I could run an extension cord rather than hard wire in a new receptacle.
The cheapo wanscam wireless ones I have are available now for less than $50. They work pretty well, can see things at night with their IR capability and they email me pics when motion detection activates at night. I could set up the port forwarding on the router to get access when away but I never bothered to do that. One downside about wireless is the newer wireless router i have doesn't reach to the detached workshop like the old one did so I had to move that camera.