I find I can do everything I need with old and OWA, and OWA is only really needed for some SP/group stuff that will probably never make it into "old". I'd switch to Thunderbird, but that's coming up short in some areas too and OWA alone won't make up the shortfall there, so my current approach is the least painful for getting stuff done, no matter how much that chafes. I find "New" to be a confusing and broken mess that is missing several key features needed to interact with other Microsoft systems (FFS!), and have fed that back to Microsoft in no uncertain terms every single time I've found myself switched to it and have immediately switched back using the feedback form they give you. No real idea on the Store version as I've only tried it once in the hope it might do everything I need (it didn't), but I hear that's awful too.
So, yeah, GP listed three products, which are the "local" versions, then there is the OWA version, so Microsoft has four totally different products that use the "Outlook" name by my count. Maybe they employed a former cola exec to lead the product development, or something; throw flavours at the wall and see what sticks? Store seems to be the "Diet" version, so maybe next up will "Cherry Outlook" and "Lime Outlook"... Personally, I really want "Outlook Zero", which will be me uninstalling it for good once I can switch to anything else.