Who's really commited to the Sprint Goal?

Don't get bogged down in the specifics. The Scrum Team commits to achieving its goals" means that the entire team commits to achieving any goals that are set forth by the team and will do any work necessary to achieve those goals.  A Scrum Team might have more goals than just the Sprint and Product goals.  They may have a goal to improve their throughput, to implement coding standards, to spend more time on Product Backlog refinement activities.  There can be many goals a team might want to achieve.  That statement is to show that it is not a single individual or even a subset of the individuals that commit to achieving the goals, it is a team endeavor. 

The place that you are quoting is only a small portion of the statement. Here is the full sentence and the following sentence.

The Scrum Team commits to achieving its goals and to supporting each other. Their primary focus is on the work of the Sprint to make the best possible progress toward these goals.

Notice the second half of that first sentence.  Also notice that there is no mention of specific goals.  Just because the word "goal' is used in regards to 2 specific commitments does not mean that those are the only goals a Scrum Team may decide to pursue.

Product Goal : it says nothing else about 

I'll point out these statements (emphasis added by me)

The fundamental unit of Scrum is a small team of people, a Scrum Team. The Scrum Team consists of one Scrum Master, one Product Owner, and Developers. Within a Scrum Team, there are no sub-teams or hierarchies. It is a cohesive unit of professionals focused on one objective at a time, the Product Goal.

All the work necessary to achieve the Product Goal, including Sprint Planning, Daily Scrums, Sprint Review, and Sprint Retrospective, happen within Sprints.

Sprints enable predictability by ensuring inspection and adaptation of progress toward a Product Goal at least every calendar month.

The Product Owner ensures that attendees are prepared to discuss the most important Product Backlog items and how they map to the Product Goal. NOTE: This was in the section describing Sprint Planning)

The purpose of the Sprint Review is to inspect the outcome of the Sprint and determine future adaptations. The Scrum Team presents the results of their work to key stakeholders and progress toward the Product Goal is discussed.

Each artifact contains a commitment to ensure it provides information that enhances transparency and focus against which progress can be measured:

• For the Product Backlog it is the Product Goal.

• For the Sprint Backlog it is the Sprint Goal.

• For the Increment it is the Definition of Done.

Commitment: Product Goal

The Product Goal describes a future state of the product which can serve as a target for the Scrum Team to plan against. The Product Goal is in the Product Backlog. The rest of the Product Backlog emerges to define “what” will fulfill the Product Goal.

An Increment is a concrete stepping stone toward the Product Goal. 

This provides a lot of detail on the importance, scope and use of the Product Goal. 

To answer your 2 questions

• Sprint Goal : it says "Sprint Goal is a commitment by the Developers" VS "The Scrum Team commits to achieving its goals". Who's right?

Both are correct.  The Scrum Team commits as a group to do the work for any goal the team wishes to achieve.  The Developers specifically commit to the Sprint Goal as it is the guiding principle in the Sprint where they do all the work, but the Scrum Master and Product Owner are also committed to aid them to be successful but helping to remove impediments, providing necessary information, managing stakeholder expectations, and more. 

• Product Goal : it says nothing else about it so, for me, and regarding the first quote, the whole Scrum Team is commited on it. Right?

Correct, the whole team is committed to it because it is the single objective that the team focuses on accomplishing with everything they do. 

Wow, thank you Daniel, it's clear and very appreciated!