Yes, CFL purports to be Compact Fluorescent Lamp, but like many things in our consumerist society, 'compact' can be a bit of a stretch:
That's a 12 inch/30 cm scale!
These are supposed to be 5500º K, 135 watt input, 600 watt equivalent light output. I believe they come out of greenhouse grow light territory and are not cheap -- like maybe $40. (Well, if you're growing the right herbs you can afford it. )
The softboxes I have are about 16x23 inches at the front, an aluminized fabric contraption held out by springy wire stays that plug into holes in the bulb socket assembly (and are a PITA to set up/take down, which is why I keep a pair set up most of the time).
There is a cloth diffuser panel behind the front panel, presumably to decrease hot spots. Front diffuser partially peeled open:
These appear to be nylon, which is OK with the CFLs, but to use hot lights, the softbox materials have be special heat-resistant stuff to withstand scary temperatures and are priced accordingly.