Assuming that you're talking about bi-directional converters, then yes, they are functionally the same.
The physical implementation may be different, tho'. Some converters are packaged with a 'D' type connector for plugging directly in on one side (e.g. RS232 connection to a PC COM port) and screw terminals for connection to external cabling.
There may also be differences in wiring associated with the RS232 handshake lines, and in the power source (sometimes an external supply is needed, while some are 'line powered', typically from the RS232 side handshake lines).
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"Love justice, you who rule the world" - Dante Alighieri
As rule it is the same device (at least I didn't meet another). As RS485 protocol is half-duplex you need as user to control state of port(open/close) and direction of data transmitting. If user wants to transmit data out i.e. for instance from PC with RS232 to 485 network, he/she has to open port for sending data out, transmit data, makes time out, switch port in data receiving mode for getting response, then it's up to user --- to remain port in receiving mode or close port at all till he/she will be need send/recieve something again.
When I said "user" I mentioned a programmer.
There are also devices which can find appropriate mode for sending receiving data automatically. This fact makes life of user much more easier.