Earlier quoted context omitted.
Substitute one for the other. The people depending on your delivery don't understand (or care) that you're doing a x-point sprint, they care that their feature is delivered.
If they "don't understand (or care) that you're doing a x-point sprint", then you have big problems, since they have to choose 'x' points worth of stories to put into a sprint, and that's one of their two key responsibilities. Also, you cannot substitute points for stories - that's the whole point of the estimation process. (and also a large part of why software projects fail. "Doing 'A' is 10x harder than doing 'B'"…
All Scrum says is that:
1) there are things on the backlog (it doesn't specific what product backlog items are or should be - they could be user stories, they could be old-fashioned requirements docs, they could be use cases - Scrum doesn't care).
2) there is a Sprint Planning Meeting where the team and the product owner agree what the sprint goal is and the team forecasts the Product Backlog items it will deliver to meet that sprint goal.
The rest is up to the team.
Teams decide to track hours or points or story counting. Teams decide whether an estimation process is useful.
Also, you cannot substitute points for stories - that's the whole point of the estimation process. (and also a large part of why software projects fail. "Doing 'A' is 10x harder than doing 'B'" seems to be hard to understand until you have points to spend
Many teams can and do just count stories. Folk like Ron Jeffries who invented the point counting / velocity concept now prefer and recommend story counting. There's a whole group of folk who eschew estimating entirely (See stuff like naked planning for example http://aaron.sanders.name/agile-fashion/naked-planning-expla...).