In what basis a micro controller or a microprocessor is classified as 8bit and 16bit?
On the basis of the word length. Most instructions will operate on word-sized chunks of data, the data bus is almost always one word wide and most registers have the width of one word.
8-bit microcontrollers have byte-sized (8-bit) words, so while e.g. computing the sum of two bytes is fast and easy with just a single instruction, summing two 16-bit values requires more thought from the programmer and will require multiple instructions.
16-bit microcontrollers have 16 bit words, so they effectively operate on two bytes at the same time. For example, summing 16-bit values will take just a single instruction on a 16-bit processor, yet you can still sum 8-bit values as usual if you want to.
32 bit and 64 bit words are also common in especially higher end processors, and some digital signal processors even have more unconventional word sizes.