Neural Radiance Fields are a technique from the neural rendering research field, while photogrammetry is a research field on its own. However these are just turf wars and in practice there is a lot of overlap between both fields.

For example, most NeRF implementations recommend the use of COLMAP (traditionally a photogrammetry tool) to obtain camera positions/rotations that are used alongside their images. So this multi-view stereo step is shared between both NeRF (except a few research works that also optimize for camera positions/rotations through a neural network) and photogrammetry.

After the multi-view stereo step in NeRF you train a neural renderer, while in photogrammetry you would run a multi-view geometry step/package that uses more traditional optimization algorithms.

The expected output of both techniques is slightly different. NeRF produces renderings and can optionally export a mesh (using the marching cubes algorithm). Photogrammetry produces meshes and in the process might render the scene for editting purposes.

Nerfs can represent reflection, speculars, refractions.

They also are proving to be faster, more accurate, etc

The input data is the same. Nerfs have the chance of requiring less input data.