The in board pads are usually clipped to the caliper piston. The outer caliper is usually placed on the carrier and held in place by the caliper (most car brakes are single piston, and the entire caliper can slide on pins to give clamping force on both sides of the disk).
Because the outboard pads are basically loose, they can vibrate and whistle or hum. Some pads have anti vibration stuff stuck to the back of the pad, or you can get greases (copper slip, mintex cera-tec etc) that add some damping to stop the vibration making a noise.
This link (not embedded the image as it’s on someone else’s forum) shows where I’d be greasing on a typical car caliper set up.
The pad can stick in the carrier, in which case you need to attack it with a file and grease the pad to carrier contact points.
And the caliper can stick on its sliders – in which case you can either play about cleaning and regreasing the pins and rubbers you have, or you can just put new ones in. There’s a firm called “brake parts” who do the refurb bits or whole replacement calipers for most cars. They’re cheaper than the likes of Euro car parts most of the time, and sometimes they’re cheaper than their own website on eBay…