To start answering this question, let's look at a more formal definition of these two terms:
Managed Service Provider:
A managed service provider (MSP) delivers services, such as network, application, infrastructure and security, via ongoing and regular support and active administration on customers’ premises, in their MSP’s data center (hosting), or in a third-party data center. -Gartner
Value Added Reseller:
A value-added reseller is a firm that enhances the value of third-party products by adding customized products or services for resale to end-users. - Investopedia
This is all sounds great, but what's the real difference between the two?
The Difference Explained
The reality is that in many ways, an MSP can be considered a type of Value Added Reseller (VAR). The term "value added reseller" is quite broad, and can be used to refer to practically any firm who performs some kind of modification or additional services before reselling an existing third-party product or service to their client. This means that countless business models could be consider a VAR, whether it's an auto dealership or an IT consulting firm.
So, an MSP often plays the role of a VAR by purchasing hardware or software and deploying it for their clients - the big difference, however, is the nature of the relationship between the firm and the client. A VAR generally works with much shorter project-based or one-off deals - the goal is to deliver the product or service to the end-user as quickly as possible so that they can move on the next sale. An MSP, however, almost always wants (and needs) to engage in an ongoing partnership with the client - it's the very nature of their business model. Reselling hardware or software may represent a small portion of their revenue, but it's generally just a means to an end: delivering ongoing IT management and support to their clients.
Also, bear in mind that some MSP's do no reselling. While it's more uncommon, some smaller MSP's may have their clients pay directly for all products/subscriptions or only lease hardware to them, so there's really no reselling happening in this relationship.
Conclusion
In short, an MSP often acts as a value added reseller by delivering products or services to their clients enhanced by their management or technical expertise. Value added resellers are not always MSP's however, and this term can be used to refer to almost any business that offers products or services to their clients on top of an existing product. VAR's typically tend to work in project-based deals, modifying the third-part product and delivering it, whereas MSP's establish ongoing relationships with their clients.
