The original NERF paper had a voxel-like grid, but instead of regular voxels with a single color per grid cell, they had an MLP in each cell that models the color as a function of position and angle.

The literal definition of a NeRF and rendering function in the original paper are a continuous non-discretized vector-field and sampling based render function.

I'm sorry, you're right. I got confused with some other papers like Plenoxels that use voxels.