Handle9:

 

C-clip is the term generically, a bit like gib. C-clip is a clipsal trademark.

 

You can also get gib mounted flush box, they also work well if you want a back on the box.

 

https://www.electricaldirectltd.co.nz/product/152-Easifix-Spring-loaded-Wallboard-mounting-Flush-Box

 

I have found them to be crap, the plastic is thin and brittle, and if you open the back up to be able to get cables in without kinking them, the box will fold as the clamps pull up to the wall surface making the gap between plate and wall even larger.