In message , Dave Poole
writes

The oak (Quercus) is a member of the Fagacaea and related to Beech
(Fagus) and Sweet Chestnut (Castanea). On the other hand, Silver
Birch (Betula) is the principal member of the Betulaceae and most
closely related to the hornbeams (Carpinus), hazels (Corylus) and
alders (Alnus). You have to 'climb' the classification tables as far
back as the super-order (Juglandanea) before oaks and birches come
together and even then they are remote from each other. In ordinary
language, this means that any relationship they once shared is very
distant indeed.

Come the latest classification (APG) oaks and birches (and walnuts) are
in the same order - Fagales. (But the APG classification tends to larger
families and orders - for example Primulales and Theales are subsumed
into Ericales - so the two taxa may well be much the same. According to
a 1997 paper birches are closer to walnuts that to oaks.

--
Stewart Robert Hinsley