In article , ned writes
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, eg cactus, succulents, trees,
etc.?


Some old (19th century) material on the topic

http://www.malvaceae.info/Literature...B/Chap1-1.html

I think the term you're looking for is herbaceous perennial.
--
Stewart Robert Hinsley