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Stock is a class where the motor specification is tightly controlled, and every eligible motor has to be checked for conformance to the Rules and have a wide availability. There are three types of Stock motor controlled in this way - 17.5, 13.5 and 10.5.
The timing on the motor is adjustable using the mechanism on the end plate to move the position of the sensors. This is allowed in Stock. All Stock classes now run with speed controllers where their timing is locked and set to 'zero'. The 12th Section run a list of these speedos that pass a test showing that their firing sequence follows the rules set out in EFRA and BRCA.
The idea of all this is that everyone can buy a motor to the same specification and race it against anyone else. As usual, the way a motor is designed within the Rules, and made, will give some differences in performance.
A Modified motor is a motor that conforms to a smaller set of design rules around its size and the way the sensors and wiring is laid out. However, there is no restriction on the wind, so Modified motors can be any wind at all. There is also no restriction on speedo timing, so many drivers running Mod use speedo timing instead of the end plate timing on the motor as it gives them more control over the motor performance.
In essence, Modified motors are in any wind from 10.5 down to 3.5. There are usually no winds between 10.5, 13.5 and 17.5 (so no 15.5 for example) as there is no point. In the US they also use 21.5 in F1 and 25.5 in USVTA - both as stock classes.
On Off-Road there is no Stock class at National level so drivers always use 'Mod' motors. Judging from advice on here, most people find something between 6.5 and 8.5 works depending on 2WD or 4WD.
Touring Car and 12th have Stock classes for their Nationals, as well as Modified classes. Things like GT12, F1 and GT10 have only one class using a stock motor - 13.5, 21.5 and 10.5 respectively - and there are other variations on those themes across the Clubs.
HTH