My background started with America military style draftsman at a Canadian firm with UK ties (Rolls Royce) then much later with Japanese firms like Hitachi, Fujitsu, Toshiba.
The funny thing, is no matter which country or foreign language , when IPC or UK or IEC standards were followed, I had no problem speed reading schematics like a book.
As I recall the distinction , which @Audioguru made , was to describe electrolytic caps , which can be polarized, P or NP ( from back to back ) , as opposed to non-electrolytic caps ( ceramic, plastic , mica, air )
Electrolytics can also wet or solid as all electrolytics follow a REDOX reaction as opposed to simply dielectrics which include all insulators.
The generic parallel plate symbol is often used for any dielectrics, but originally just for non-electrolytics.
if a large cap was intended to be shown, then a curved side ( to suggest cylindrical construction) symbol would be used and if polarized then the (-) side was uniquely identified by either a distinguishing bar (dark or curved) like a bar on the component for (-) otherwise a (+) on the symbol or a (.) dot on one side the part. ( e.g. muher)
All insulators are dielectrics and all dielectrics are insulators and both are capacitors when enclosed by separate conductors.
But only "electrolytic" caps ( including Tantalum wet or solid) used the unique symbol.
IMHO the CAD packages started the drafting method with the same -||- symbol for all and any type of cap with (+) if polarized.
In any case , the user ought to be aware of the relevant standards they wish to follow depending on their client or the contract or their awareness of IEEE/ ANSI/ IPC /IEC / Mil-Std-Hdbk standards.
I recommend IPC-2612-1 "Sectional Requirements for Electronic Diagramming Symbol Generation Methodology"
Most often small companies just use whatever tools they have and invent their own stds depending on the draft peron's skill and experience, which may depart from the now agreed international IPC standards.
It's all about clarity and a common communication symbology.