(I, on the other hand, have to be reminded that 50 years have passed.)
Edit: as someone below mentioned there can not be a 'Standard Forth'. You just write your own one as you see fit.
Forth is a collection of ideas and philosophies toward programming as much as it is a language. Two stacks and a dictionary. Threaded code (direct, indirect, token, subroutine, etc...). Collapsed abstractions. No sealed black boxes. Tight factoring.
C has changed. Forth is everchanging.
The stacks are likewise a description of semantics rather than implementation. Some Forths keep the top few stack elements in registers to reduce overhead. If the return stack isn't user-accessible (r> >r etc.) then, again, you're straying closer to a higher-level functional language than a Forth.
There are many kinds of threaded code. For example, subroutine-threaded code uses native subroutine call instructions in word bodies and does away with the inner interpreter. Threaded code is a natural consequence of disentangling conventional "activation records" into two stacks which grow and shrink independently. You could have a Forth without threaded code, I suppose.
Some Forths attempt to "seal off" or otherwise obscure some parts of their own internal workings from "user programs". This is more common among dialects which try to adhere to ANS specs, like GForth. This isn't a total anathema to Forthiness, but it tends to introduce additional complexity. If a word is useful for implementing a forth kernel, why couldn't it be useful in implementing other functionality, too?
If you're building something higher-level which vaguely resembles Forth, it's probably better to describe it as a concatenative language. A dependent type system doesn't sound very Forthy, imo.
VFX Forth from MPE UK is a native code generator. It evaluates source code and emits inline code or calls depending what you tell the compiler to do. It can expand everything to inline if you tell it but your code would get much bigger.
This is the state of the art for Forth compilers today.
Homemade systems and older systems use threaded code.
I have no affiliation with MPE.