A sponsor is a stakeholder, but not all stakeholders are sponsors. Sponsors are biased towards supporting the project and will benefit in some way from its successful execution. A stakeholder is someone with a vested interest in the execution and outcome of the project. This includes people who may not be in favor of the project, but whose actions or inactions could influence project success.
A sponsor is usually someone in a significant leadership position who has asked for, or provided an endorsement for the initiation of a project. They may also have provided either internal resources to execute the project or they may have an influencial relationship with an external customer who has authorized and funded the project.
A stakeholder is anyone involved in the execution of the project or anyone who may be affected by the project performance and outcome, either favorably or unfavorably.