I've learned about microcontroller and the teacher taught me a few instructions in AT89C51. At first I though it was assembly but then I realized
if it was assembly, the file type should be .asm not .a51 so I was really confuse, what is this language, are they both the same?

 

There are all kinds of different assembly languages, even for the same architecture. Beside the literal instructions in the processor's instruction set architecture, you have all kinds of other things that a particularly assembler supports such as pseudoinstructions, macros, symbolic labels, and other stuff. Often times they will use the generic suffix .asm but that means that YOU have to keep track of which assembler can assemble a particular .asm file. Other times they use a different extension to make that easier, or to tell the assembler which variant of the language that file is supposed to contain.

 

http://www.keil.com/support/docs/752.htm

http://www.keil.com/support/docs/2094.htm