What makes a rectifier diode and an LED

In a rectifier diode, there will still be some e-h pairs that recombine. However there are reasons why they don't produce light

Firstly, Silicon is an indirect band-gap semiconductor. What this means is that the energy levels in the band-gap don't line up nicely making it very inefficient at emitting photons. Generally recombination will take place in a way which results in either vibration/heating of the silicon lattice, or other means (e.g. transferring the energy to other carriers). It is possible for silicon to emit light, however it is very inefficient.

Secondly, the band-gaps in rectifier diodes will not have the right energy level for photon production. Remember that the frequency of a photon is proportional to its energy (\$E_{ph}=h\nu\$). To produce a photon of a given colour, the semiconductor band-gap energy must be approximately equal to this energy (i.e. \$E_g = E_{ph}\$).

Thirdly, the doping levels of rectifier diodes will be much to low. Lower doping levels means fewer carriers which in turn means there will be less recombination of e-h pairs than, say, a heavily doped LED p-n junction. This is evident from the fact that the forward voltage of the rectifier diodes is much less than an LED (doping levels determine the built in potential).

Finally, LEDs are fabricated in a way that there is an emission surface from which photons can be emitted (a so-called "heterostructure"). Without this, the emitted photons would just be re-absorbed. This surface is then encapsulated in a transparent lens to get the light out efficiently - and to minimise the number of photons which reflect off the semiconductor/air interface back into the device. Rectifier diodes do not have any of this - they are sealed in opaque epoxy packages.