The question was asked ".......Is there a botanical expression or
definition to distinguish between, perennials which die back each year, but
regenerate from the old rootstock, and perennials which do not die back,
e.g. cactus, succulents, trees,
etc.? .............."

Interesting,
The term herbaceous perennial tends to be used to cover both plants that die
back for the winter such as Phlox, Michaelmas daises etc as well as such
plants as Pinks,Wallflowers such as Bowles Mauve etc which hold their leaves
all year round.
Checking back through my old "Bible" the describe Herbaceous as A word
which means herb like growth. It is applied to plants which bear stems which
die down to the ground annually.
Whilst Garden pinks are described as "Garden plants".


--
David Hill
Abacus nurseries
www.abacus-nurseries.co.uk