Are the terms for brain divisions based off of embryonic development (e.g. prosencephalon, diencephalon) used for mature brain divisions? (e.g. forebrain, interbrain). For example, would it be wrong to say that the cortex of an adult human a part of their "prosencephalon"/"telencephalon"? I've seen texts refer to the "telencephalon" of an adult brain, though it has mostly been in a developmental context--and from my experience I haven't seen it explicitly stated when to use either term so I'm not fully sure if they're synonymous.
From my point of view, the terminology regarding the early three vesicles prosencephalon, (forebrain), mesencephalon (midbrain), and rhombencephalon (hindbrain) as well as the later developmental structures arising from these structures, namely telencephalon, diencephalon, mesencephalon, metencephalon, and the myelencephalon are mainly of use when discussing embryonic development. Alternatively it can be sensible to group various brain structures according to embryonic origin when discussing, e.g., infants with developmental brain disorders, with the origin very early in development. In this case the congregate of brain structures arising from an early embryonic vesicle may be affected.
I have seen authors swinging around these anatomical terms outside the context of development and quite frankly, it often doesn't make sense and only complicates matters as one has to trace back the structures arising from it later in life. Not being an anatomist, my humble opinion would be, wherever possible, to avoid these terms.
For school or college level biology class these hierarchical classification schemes (based on devbio) are still sometimes used and it helps me greatly to conceptualise the brain structure and basic folding as well as to get a meaningful mental framework to put the so many other small parts of brain.
Learning about a smaller brain part (say for example the parietal lobe, or for say hippocampus or amygdala or superior colliculi etc) and not knowing whether they belong to prosencephalon or mesencephalon or telencephalon (or some other level of structural hierarchy) will make me feel afraid and bizarre, and i would also fail to conceptualise and visualise the zones. the names of zones will appear like a chaotic crowd of plastic balls.