What is the biggest difference between "traditional" partner marketing and influencer marketing? Are there any lessons from influencer marketing you can apply to agency/services partners?

There are many differences. Partner Marketing is a collaboration between two companies, two businesses or brands. Influencer Marketing is between the brand and an individual. Partner Marketing can sometimes be based on an exchange of resources or deliverables, not necessarily money. Influencer Marketing is transactional by nature. The brand pays the Influencer to create content and distribute it to their audience. Having said that, Influencer Marketing is very similar in the sense that the relationship and trust is the foundation of the partnership.