There is no difference between "HOA" and "Pure HAO", but I think you maybe meant to ask what the difference is between "Raw Ambisonics" and "Pure HOA" ...?
1. HOA is an abbreviation that stands for "Higher Order Ambisonics". HOA up to the 3rd order was introduced with the release of MIR 3D. Previous versions of MIR only offered 1st order Ambisonics - the most "primitive" variety of Ambisonics, if you want, but also the one that's most easy to handle and to understand.
2. The category "Raw Ambisonics" is used for a small selection of special Output Formats for MIR 3D that bypasses its internal Ambisonics Decoder (like mentioned before). MIR's output will be raw Ambisonics of the chosen order and has to be decoded externally for meaningful results. It's also indicated by an "empty", direction-less Ambisonics sphere in the position of MIR's Main Microphone:
3. For some of MIR's Output Format presets I used the term "pure HOA" to indicate that the decoding relies on a plain spherical, "coefficient-based" approach (i.e. on virtual loudspeakers instead of the more obvious virtual microphone capsules). Sometimes I used the term "straight HOA" synonymously.
4. For aesthetical reasons, some of my presets rely on mixtures of a "pure" HAO approach and added virtual capsules of lower order. This should always be reflected by the info text in the Output Format Editor, and of course by the graphical representation of the mic shown in MIR's Venue Map:
HTH!
PS: Please don't mix subjects within one forum thread. Keep your Logic issue separated. Ideally you will contact VSL's support and ask them to look at it. Thx!
/Dietz - Vienna Symphonic Library