A photo-diode directly connected to 50 Ohms is a solution for relatively large, fast pulses, but not that much for a low level DC signal. One can usually increase the resistor to get more like some 100 mV without to much extra DC error. Than a more normal DMM is OK.
For a 50 Ohms source or a thermocouple (often similar impedance) the amplifiers bias is not so critical an most AZ OPs are OK to build an amplifier.
Electrochemical cell voltages rarely need to be measured to µV resolution, as there usually is quite some temperature effect. However here one may need high impedance. So the suitable amplifier would be more like a good non chopped OP (JFET or CMOS input depending on whether noise or bias is more important). If a chopper, than more like a low bias type like max4238 or LTC2054, not so much the low noise ones.
The two examples are quite different in source impedance and thus essentially need different amplifiers / front ends. The usual DMMs are more like good for something in between, so not really good for either case, but maybe still acceptable.