Well technically there are NO standard functions in C/C++. All functions need to be included.
The Arduino "library" adds functions like digitalWrite and Serial.begin.
Instead of the standard libc, avr-gcc compiles in avr-libc for many of the "standard" C-type functions.
I'm not trying to understate the Arduino functions. However, they aren't magic. Just look at the source code included with the IDE. (Java/hardware/arduino/cores/arduino). You can see how functions like digitalWrite() work.