I have a Raspberry Pi hooked up to my TV and whenever I need to control it from my laptop (getting and interacting with the same screen on my laptop that I see on my TV) I have been using VNC. It is quite slow. Would this work better for that use case or is it really intended for something different? (And if the latter are there better solutions than VNC for what I want to do?)
If you can look at your TV instead of your laptop, I highly recommend using KDE Connect
Yes this will give you similar results.
There's VNC and VNC-likes (rdp, steam link, rustdesk, etc) which all do similar: stream a screen, allow remote keyboard/mouse, maybe redirect sound, maybe use video encoders.
There's also things like deskflow, which allow you to use one keyboard/mouse and control with multiple machines.