Plain has the meaning without embellishment or bells and whistles or additional features
Pure has the meaning without other ingredients
this code is pure C
is correct if the codebase is only in C and nothing else
Plain C is usually as specified by Kernighan and Ritchie, other flavours of C will depend on the compiler implementation, for example how macros are handled or compile time variables or object handling.
Another example would be orange juice:
Plain orange juice can be thought of as the juice from sweet oranges and is the official orange juice of Florida. Fancier orange juices may use blood, valencia, or mandarin oranges as their source.
Pure 100% orange juice would be juice from only oranges without any additives and is sometimes referred to as fresh squeezed when appropriate. Orange juice additives may include calcium, omega-3, vitamin-D, anti-oxidants, as well as other fruit juices. A popular addition to orange juice is vodka and the result is called a screwdriver.
For your algebra example
may refer to what is more technically called elementary algebra also colloquially called simple algebra or high school algebra to make the distinction with