It is true that the Sprint Backlog is a result of Sprint Planning, and it includes the Sprint Goal. This is because:

Sprint Planning is an event where the Scrum Team plans for the upcoming Sprint. The purpose of Sprint Planning is to align the entire Scrum Team around a common goal and a plan for delivering an Increment that meets that goal.

The Sprint Backlog is the set of Product Backlog items selected for the Sprint, plus a plan for delivering them as a “Done” Increment. The Sprint Backlog is owned by the Developers who use it to organize and manage their work during the Sprint.

The Sprint Goal is a short-term objective that provides guidance and focus to the Scrum Team throughout the Sprint. It is a flexible and negotiable commitment that can be adjusted as more is learned throughout the Sprint.

The Sprint Backlog is created by the collaborative work of the entire Scrum Team during Sprint Planning. The Product Owner proposes how the product could increase its value and utility in the current Sprint. The Developers discuss how they can deliver a “Done” Increment that meets this proposal. Together, they define a Sprint Goal that summarizes why the Sprint is valuable to stakeholders. Then, they select enough Product Backlog items from the top of the ordered Product Backlog to satisfy the Sprint Goal. Finally, they create a plan for how they will deliver those items as a “Done” Increment.

References:

[Scrum Guide], page 14, section “Sprint Planning”

[Scrum Guide], page 15, section “Sprint Backlog”

[Scrum Guide], page 15, section “Sprint Goal”