Thanks Westaust55...I'd already been down this road, and those links only further reinforce my idea that in Serial comms such as the PICAXE is using (only two possible bit states, 1 and 0) bit-rate = baud-rate.
Yes and no.
The encoding system used can result in variations, too, as strictly speaking the baud rate is determined from the number of characters transmitted in a given period of time and the average number of bits per character, and different encoding methods can mean there are differences.
Also, because traditionally the baud rate was measured from the starting edge of the start bit (a falling edge in conventional serial comms) to the centre of the last bit in the character, divided by the total number of bits in the character (including start and stop bits) there can be a variation from bit rate, where a consistent edge is used to make the measurement.
As I alluded to before, this all goes back to the way the RS232 standard was derived and the old Baudot encoding system that started it all. The system worked by using the edge of the first start bit to de-clutch the transmitter drum (so timing starts on an edge), with the detection window of the receiver set to a time interval that should correspond to the centre of each bit. The result is that the time from the edge of the start bit to the centre of the detection window can be longer (by half a bit width) than the time between detection windows.
Technically, therefore, baud rate and bit rate can be different. In practice, given the way that things have developed this need not be the case, as you say. If you want to ensure universal compatibility using serial comms, it makes sense to ensure that the tolerance on timing is sufficiently broad to cover both the "in spec" standard (start bit edge to initial data bit centre) and variations where detection windows are all the same width. Also worth noting that the RS232 (or whatever name it has now) standard isn't that tight, and allows a fair bit of leeway (it also refers to voltage levels that aren't now that common for the sort of serial comms we tend to use).