After a lot of rooting around on the net, I've figured out (I think!) what's going on with the names.
It seems that 'serissoidea' would be the correct term to use if any, which means 'all species of serissa'.
see here
Anyone conversant with latin may be able to correct me (or confirm).
Anyway, MY particular tree has glossy green leaves, tiny star-like white flowers, therefore it appears to be
Serissa feotida 'snow rose'.
see here
All this may seem irrelevant and/or obvious to many
but my wife
does call me a fuss-@rse sometimes (well, I
say sometimes, I really mean often...
)
Regards,
TB