"what is the difference between PC's serial port and 8051's serial port?"

The PC's serial port is an RS232 port; the 8051's serial port operates at unipolar, 5V (or whatever) logic levels. Therefore, the 8051 needs an RS232 transceiver (MAX232 etc) for connection to a PC or any other RS232 port.

The 8051's serial port can be configured to several modes that are not compatible with a PC;
The PC's serial port can be configured with some settings that may not be compatible with the 8051 (eg, No of data bits).

You must ensure that both ends of the link have the same format!!