@KennethLavrsen is perfectly correct. To summarise
Frigate - software to connect to cameras and create an nvr. Has a web interface UI.
Frigate addon - run frigate on your ha machine if it runs haos or supervised ha.
Frigate proxy addon - if you run frigate on another server get it’s UI on ha, with a side bar icon etc
Frigate integration - get frigate related sensors in ha, so you can turn a siren on when a cat crosses your driveway.
Frigate UI card - get a nice frigate interface in Lovelace. This is not the native frigate web UI. Edit: this card can also be used with other cameras that are integrated in your home assistant.