What is difference between single and common cathode configuration? If I want to use 2804 for rectifying, will it act as 2800?
As you can see in the table, every package has identical single diode specifications.
But your question is "If I want to use 2804 for rectifying, will it act as 2800?"
The temperature rise will be double sharing one package for two diodes.
Answer: Yes for peak currents <=1mA
No , if near Ip=10mA do not use if temp rise exceeds 70'C above worst case board temp.
Although they have identical characteristics, now it means the dual diode package must share the same thermal resistance of;
500°C/W for SOT-23 and 150°C/W for SOT-323
You must work out the temp rise, but it means your DC load must be << 1mA since the diode peak current into a storage cap with 10% ripple will be 10mA