I purposely didn't correct this earlier to save you foreigners
Dog box is sometimes used to refer to a racing gearbox over here - this is because a lot of people in England used to automatically assume that a racing car would have 1st down and to the left as per Dog-leg gearboxes, as most after market race-boxes were built this way - This used to be done as it's the most efficient pattern for a 5 speed manual gearbox, so was viewed as a 'free' performance boost to the car (race cars only need 1st once normally for an entire race, so It's stuffed into a corner on it's own). Even if 1st is needed on a lap it will be fairly rare compared to the other gears.
A Crash box is anything with straight cut teeth, as it will crash and crunch for any change that isn't perfectly matched in RPM's. While a crash box will survive non-matched shifts fairly well, that isn't their intended purpose and you can still blow them up easily enough if you don't use the clutch. (Trust me - I've pushed enough of them off tracks while marshalling
)
Nearly all race gearboxes are crashboxes as they use straight teeth. Also most older lorry, off road and construction equipment use crash boxes for their toughness/torque transmission.
This is less common nowadays as CNC machining is so much better, and structural science is so much further advanced that the 'impossible' (automatic gearboxes on big lorries for instance) is now pretty much normal.
Dog-Leg is any gearbox that has 1st down and left (Or down and right for reversed orientation gearboxes like the BRM monstrosity from the P83/P115) with reverse where a 'normal' gearbox has 1st.
So most old BMW's/Bigger engined old manual Mercs, some 5 speed Porsches (I think) use them. Also lots of Getrag boxes aimed at racing/performance up until the 80's were dogleg for instance (The manual version of my old 280TE was a Getrag dogleg - only time I've ever wanted a manual Mercedes
Oddly an old Merc van I drove in a job I had about 20 years ago had a dog-leg gearbox - ironic as it had almost no performance!)
In the Capri on-board I posted earlier you can see it has a dog-leg box - standard Capris' had 4 or 5 speed conventional gearboxes on the road with 1st up and left.
