From the what I understand, the FAGGA basically expands your maxilla forward. Here's a good example [1] that shows the appliance in action. The photos showing the upper jaw after FAGGA insertion match my experience.

The ALF can be applied to both the maxilla and mandible (whereas the FAGGA, I believe, is just for the maxilla), but the growth it promotes is more gradual and subtle.

I don't think either appliance shares much in common with lingual braces, functionally speaking. I'm not a doctor, but from what I understand lingual braces act primarily on the individual teeth whereas the ALF and FAGGA act primarily on the jaw bones.

[1]: https://www.robinatowndental.com/jaw-expansion-without-surge...