I don't know but my instinct tells me that they must do. It may have changed since I went through but my recollection is of having to submit an 'Application for a Commission' form prior to RCB and that that form was fairly intrusive; intrusive to the extent that 'type of commission applied for' was almost certainly a part of it.
Should it matter whether an individual is applying for a regular or TA commission? Again, my instinct tells me; yes, it should. That is not to say that officer qualities should be any different between regular and TA officers (indeed, you should not be able to spot the difference in a line-up), only that there are, I suggest, fundamental differences in what is required of regular vis-a-vis TA personnel in terms of commitment throughout their respective careers. For regular personnel, a willingness to give up your day job is obviously one of them.
TCB and RCB have gone, there is now a common Army Officer Selection Board (AOSB).
Some are run at weekends, some during the week; the weekend ones are intended to be for the TA, but there is no reason in theory (except that the weekday ones get booked up very quickly) why any candidate shouldn't attend at any time.
Obviously Westbury will know your background, so they will know if you are TA. Plus, if you are there on a weekend it will be a bit of a giveaway.
However... the board is the same, the standard is the same and if you pass AOSB, weekend or weekday, you can be an officer in the British Army. One army, one selection. If you're not good enough to command Regular troops on operations, you're not good enough to command part timers on operations either.