A car with a Scalextric Digital chip will not run on a Carrera Digital track, nor vice versa. But, you can install a Carrera Digital compatible chip into a Scalextric car, or any other brand of car.
This is the biggest problem with digital where there is no uniformity between the different brands because each brand’s digital system is different and not compatible with other companies. If you want to run a Scalextric digital car on a Carrera digital track you have to change the chip. The same if you want to run a Carrera digital car on a Scalextric digital track you have to change the chip.
Incompatibility is also because Scalextric SSD lane changing is handled by car and Carrera lane changing is a function of the powerbase.
Scalextric Digital Plug Ready (DPR) cars can be converted to Carrera Digital 1:32 using the Carson 500707130 Digital Plug Scalextric (EasyFit) for Carrera Digital 132. It's a quick, non-solder, 60-second job and can be swapped around.
Carson fits Scalextric DPR cars but do not fit formula 1. The Scalextric decoder is fairly small and there are two types: one for the small F1 hatch, another for the larger DPR hatch. There is no reason, other than size, that you couldn’t shoehorn a Carson decoder into a non-DPR car, but be prepared for some level of DIY such as cutting/soldering wires.