The progressive-left uses the term "neoliberal" as a disparagement for free-market classical liberals, who in turn reject the term for themselves.
Non-ironic "neoliberals" use the term proudly for themselves, and do so as a way to signal their own rejection of free-market classical liberalism in exchange for a managed-market technocracy.
And the people on the left who use the term "neoliberal" disparagingly are largely in agreement on most of the managed-market technocratic policies favored by the non-ironic "neoliberals" who use the term willingly, thereby uniting both in opposition to the free-market classical liberals who want nothing to do with either of them.
Friedman used it in a “positive” sense of meaning the free market system.
On the other hand, Mises used it as meaning the interventionist welfare-statists who opposed a free market but who had appropriated the”liberal” label.
The term seems appropriate in Friedman’s case, because of his embrace of monetary central planning (as Keith Weiner mentioned above) and of the pseudo-Keynesian aggregate demand-management macroeconomic paradigm. As fond as I am of him, those two positions alone were more than enough to make him not a classical liberal, and to warrant the prefix “neo”.
Concerning Richard von Mises — the famous expert on fluid dynamics and probability theory, and member of the Vienna Circle — I cannot imagine on what basis besides animosity and wilful churlishness he would describe his brother as a neoliberal rather than a liberal. Surely he understood his brother’s views perfectly well (i.e., knew what they were), and knew there was nothing “neo” about them. And knew his brother had been a lifelong champion of liberalism, specifically and explicitly.