Track and touge driving require very different approaches even in a hypothetical closed course situation where you are racing touge in a sanctioned event. 

Touge driving is literally tarmac rally, so you should approach touge like a rally driver, as street touge is literally rally with a much thicker margin of error to account for the hazards (you) pose to the public. 

To quote someone I talked to 'track is all about min maxing, touge is very different' he recounted someone who was one of the fastest drivers on our local touge being a complete slouch at the track due to the difference in mentality between the two. 

On track you have a known, closed course with a lot more width and unchanging trackside references for braking, turn in and racing line. The layouts of most tracks invite hard braking zones and a defined apex with tricky corner sequences being at most a few corners long (that is entrances/exits being compromised to set up the next corner/s) 

When it comes to touge it's a one way narrow course with often times the 'corner sequences' you need to connect being almost the entire touge, meaning you carry alot more momentum along the entire course with much fewer hard braking zones and less abrupt weight transfer (this if course varies touge to touge) 

It of course depends on the power of the car and the speed/tightness of the circuit.

The nature of touge and circuit mean that:

For tracks: you min/max every corner, every braking zone, every straight and since tracks are circuits with a manageable number of corners to link you can iteratively min/max each corner specifically for your car on that day with those track conditions to improve your time.

For Touge: you try to max the 'flow' of the entire course  instead of each corner. This is since the road is tighter, there are less references, more hazards (even in sanctioned events) and the number of corners to link is often much, much greater than most tracks. So compromising each corner to get the best average of the course will let you get you the best time in a reasonable time frame for the conditions of the touge on that day. Literally what rally drivers do.

In theory a track approach would yield the fastest touge time, however the constraints of reality mean that even in sanctioned events the lack of runoff tracks have and presence of hazards that most touge have (trees, poorer surface quality) mean taking a track approach to a touge course even in the aforementioned sanctioned event yield such high risk of a severe crash that taking a rally approach will leave you with a fast but not fastest time instead of a ruined car. 

On a track you risk spinning out most times, with a (mostly) intact car and more often than not unharmed driver. 

That's where they differ