I know that texelFetch performs a lookup using texture coordinates with range [0, textureSize], and textureLod with range [0,1] both with explicit level of detail.
But I have noticed that textureLodOffset requires an offset as ivec2, int and so on. This seems to be the case for texelFetchOffset as well.
I can see why this makes sense for texelFetch, but I am not sure how it relates to textureLod.
I am used to computing the offset coordinate manually in the shader with something like coord.xy + 1/textureSize() for textureLod. I don't think this is causing any issues with performance etc, but I would like to know how we can use textureLodOffset with integer coordinates as specified in the documentation what makes their use different from texelFetchOffset.
The difference between textureLodOffset and texelFetchOffset are the texture coordinates.
The texture coordinates of textureLodOffset are in rage [0, 1]. But the unit of the texture coordinates of texelFetchOffset are texels and the range of the coordinates depends on the size of the texture. In compare to the *Fetch* functions, textureLodOffset respects texture filtering and sampling.
The *Fetch* functions performs a lookup of a single texel from an unambiguous texture coordinate. See OpenGL 4.6 API Compatibility Profile Specification - 11.1.3.2 Texel Fetches
In both cases, the offset argument is integral because it is meant to access neighboring texels. See further OpenGL Shading Language 4.60 Specification - 8.9.1. Texture Query Functions.