RAW = RAW data from the camera sensor, meaning you can change all digital data after like white balance, iso, contrast and so on. With RAW you get muuuch more information to work with in post and can bring forward greater details that else would be impossible.
I don't know if the other users are talking about unprocessed images with RAW (the format the videos are when saved from the Theta S) or processed RAW (360-image with RAW information in the image).
HDR = High dynamic range. You get more information in the highlights and shadows. If you shoot on a bright day the final shot doesn't get overexposed or underexposed. This you have already implanted but I wanted to say so you know the difference between HDR and HDRi (from what I think I know).
HDRi (from what I think I know) = A technique used when lightning and adding reflections to 3D models. A HDRi image contains multiple 360 images of different exposures. For the naked eye you won't see all the information inside the image but a computer can use this extra information to calculate the brightness and color of different objects in the image.
Eg, The computer can see that the sun is MUCH brighter than a lamp in the same image by looking at the different exposures while for the naked eye they are both as bright.
So HDR is for the eye while HDRi is for the computer.
This technique is a gigantic time-saver and everyone is using it from beginners to the top in Hollywood.
Right now I'm in the middle of a feature film and we picked the Theta S to shoot the HDRi images instead of taking 50 images alone with a camera. It's a great time saver but it could become even better if the processing could wait till after all photos is done. As said before, if we could get the unprocessed photos from the Theta S (could be a API setting only so the "normal" users won't get confused and shoot images they don't want) and later process them with the Theta software.
There is not a need for RAW for HDRi but it would be a great extra to make the images even better! But from what I read in another thread, RAW would be difficult to implant, implanting the feature to take unprocessed photos would be a great thing for the Theta S and would open up a lot of new usability-doors!
Being able to take unprocessed photos and later process them through the Theta software would open up for a lot of usabilities like HDRi (post-processing with all images in another software) used by everyone!
If later being able to shoot unprocessed RAW would be a dream come true!
If you have any other thoughts or questions, don't hesitate to ask me!