An endorser is any person who has established authority and can vouch for a product or service or an idea. An endorsement can be considered a certification. It can only come from a person with a certain amount of authority. It is almost like saying "I am telling you that this product is good, or you should support this service or cause." A good example of endorsement is movie stars appearing in cosmetic products advertisements. Often, endorsements are paid assignments. More often than not, viewers see endorsements as commercial engagements. And, this commercial aspect makes the endorsements less credible.
Influencing, on the other hand, is rooted in peer-to-peer recommendations. There is no obvious commercial connection between the brand or service or idea and the person making the statement. This disconnect makes the statement more credible. The 'authenticity' factor is high. Anybody can be an influencer as long as they have large number of followers and their followers want to hear what they have to say.