DVRs are devices that record shows and sometimes have functions that allow fast forwarding or rewinding. They sometimes have a function to pause or play recorded shows or even recorded shows. Tuners are devices that allow you to tune or convert a signal (PayTV or Free OTA Broadcast signal) to a format that can be interpreted by a TV or Streaming Device.
NOTE: DVRs without a HDMI or Composite connection that plug into the network have no way of interacting with your tv unless you have some sort of streaming device. This can be a good or bad thing but purchased without a streaming device can be a costly mistake, so beware