Mike, you're using the term 'synchronous' in a way that doesn't make sense to me.

I have no idea of your relationship that you've drawn between fixed number of characters, TCP and communicating with modems.

Your basic RS232 communication between your PC and your 8051 board is asynchronous. There is no common clock between them, however both units clocks must be within a certain percentage of each other in order for communication to take place - the clock in this instance is the bit clock or baud rate generator which is usually 16x the baud rate. The uart hardware takes care of the transport of 8 bit values.

Next we have the concept of synchronism of data between two units. To transfer data in blocks, we usually packetise the data - we add information to enable the transport of the required data and so the receiving end can findthe start of our data. This allows us to 'synchronise' the receiving end so that it can check the received data and process it. There are various methods for this - some examples are PPP and SLIP. I suggest you do some Googling to find out how they achieve their goals.

Then the TCP or UDP packets are 'encapsulated' in SLIP or PPP packets to send via RS232 whereas in the case of ethernet, the TCP or UDP packets are encapsulated in ethernet or 'MAC' packets.