HP and HPE are now two separate companies, split from post-Fiorina HP.
HP does consumer grade stuff only, while HPE does the enterprise side (not just consulting, in fact non trivial portion of HPE consulting arm was spun off and merged into DXC)
I agree with your point, and want to add that HP does commercial grade end-user compute and printing along with the related enterprise services. They have a whole set of offerings for the medical industry [1], industrial printing [2], and enterprise PC fleet management services [3].
That depends on which trail of awesomeness you are after.
The trail that maintains the legacy of DEC and Silicon Graphics and Cray is in HPE (where I work). The Cray legend is still very much alive, but you can still detect the whiff of the the spirit that made HP and DEC minicomputers extraordinary.
Well, I suspect the SGI legacy is now in better hands than when it was controlled by Rackable with branding filed off. The only good parts they sold us were the Ultraviolets, and those were probably the most nonsensical purchase (protip: do not buy supercomputer modules just to run 8 VMs on it, it's waste of money even if the hw is awesome)
HP does consumer grade stuff only, while HPE does the enterprise side (not just consulting, in fact non trivial portion of HPE consulting arm was spun off and merged into DXC)