Ron Jeffries is generally considered the creator of story points, from which velocity is derived.
His "Story Points Revisited" article is a worthwhile read.
https://www.ronjeffries.com...
"Story points" are a relative sizing of the effort, risk and complexity of the PBI, at least as I coach teams. Use them if they're helpful. Story points are not attributes of each individual's tasks rolled up to accomplish a PBI.
Velocity is simply story points delivered over time, assuming your team is not using some 1 point = 1 day type of approach as is common in SAFe implementations. Velocity should vary. In practice it will have an average over time for stable teams with stable work. I don't see that stability a lot in the gov space where I work. Velocity should be used very, very cautiously, if at all, to gauge capacity for sprint and/or release planning.
"Value" is not Velocity. Value has many aspects: customer value, market value, user value etc. Value can be calculated in dollars, subscribers, time-saved, increased quality, customer delight/happiness and many other ways. Find what moves the needle in your organization.
Knowing the relative effort, risk and complexity of a PBI along with its anticipated value, teams and organization can make smarter decisions on what to build next.