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The most common C library is the C standard library, which is specified by the ISO and ANSI C standards and comes with every C implementation. ("Freestanding" [embedded] C implementations may provide only a subset of the standard library.) This library supports stream input and output, memory allocation, mathematics, character strings, and time values.
There is no difference.
Embedded C just means that the application is going operate something like a washing machine, cash till, engine management system etc. like a stand alone application as opposed to a program running on a PC.
There is a major difference in C & Embedde C.
Embedde C is basically meant for embedded system. So, for Embedde systems we have constraints on memory, MIPS & porting on other platforms without any major hassels. but normal C can be used in any application. the same you can't use for Embedde Systems.
C is C. No difference between C for desktop or Embedded. The only difference comes from the C library implementation on the cross compiler. Sometimes not all functions in the C library is not implemented in the cross compiler.