Numerical markings have different sub-units for capacitors than for inductors, am I right ?
For capacitor, a marking 473 is in pico farads, and
in an inductor, a marking 473 is in micro henries.
A capacitor marking 680 can be 68 picofarads ; or if the part is old, can be 680 picofarads, right ?
There is no numerical markings for pico henries, right ? Nano henries is not used either, right ?
Do you mean, that inductors in the pico and nano henry range do not exist? Inductors go as low as 100 pH for high frequency applications. SMD types are widely used in this range, and inductor/capacitor cases like the 0402 and 0603 do not have any part markings.
As you mentioned, the markings may not be following a standard. The safe procedure is to consult the manufacturer datasheet (in case of new designs) or measure the capacitance/inductance value (in case of old equipment repairs)
You're right about the first part. The *expanded* number is in picofarads, and by "expanded" I mean the number after applying the multiplier.
The second part is not correct, however. The *expanded* number on inductors are in microhenries, so 473 on a choke would be 47000uH, which is the same as 47mH.