Ok I get it now. You never regeared your subaru. If you did, you would have had the same issues. Re-gearing is not an easy job. There are a few things that you are not used to because you are not coming from axles separated from the transmission.
Axle housing - Metal housing
Carrier - holds the ring gear (it bolts to it) and has spider/other gears inside
Pinion Gear - sits in the housing, is responsible for changing the drive shaft rotation force the ring gear
Axle Shaft - the shaft that slides into the side of the differential carrier that goes from the carrier to the wheels
Differential - A term used that usually means the entire "pumpkin" of the axle housing (without the tubes). Really it just means there is a change in gear ratios within this component.
When you say buy a differential, this is where the confusion is. You can not buy just the differential. Either you buy an entire assembled axle (new/used) with the gear ratio you want, OR you have to buy all the components and install them in your axle housing.
Setting up gears are required anytime you change gears. Think about your picture. The ring gear can move closer to or farther away from the pinion gear (using shims on the entire carrier). The pinion gear can also be moved in and out of the housing. There is a gear pattern you are trying to acquire (picture below with the yellow gear paste). And you want specific pre-load (amount of force required to turn the gears). You also have to setup the pattern for BOTH sides of the ring gear (drive and coast side). There are specs, but it honestly will cost you time and possibly damaged parts if you try to do it yourself the first time.
This image shows all the possible adjustments: