Unique Value Proposition is customer focused, differentiation of services is product focused.
In sales and marketing, to introduce your product or service to a potential customer most effectively, you have to create a perception of "differential advantage". That means you have to describe it in a way that 1) differentiates it from others, AND 2) builds positive perception of value. Part (1) is differentiation of services, part (2) is unique value proposition. Rolling (1) and (2) together effectively in a word or phrase is what branding is all about.
A UVP is essentially a description or encapsulation of the value to the customer of doing business with you rather than anyone else. The focus is on the VALUE of the benefits that you bring to that customer's situation, rather than on the benefits themselves. In its "elevator speech" form, it is the generic gains that your target market will achieve from being involved with you, gains that they can't get elsewhere.
Differentiation of services is more about the branding of that UVP. If the UVP is the unique "WHAT" that my customers gain from this, differentiation of services is the unique "HOW" my services deliver that "what". The focus is on the features and benefits of the PRODUCT/SERVICE itself that are different from the features/benefits offered by competing products. And it is the "personality" that you want your product/service to be remembered for. The label or tag or mental short-cut that you associate with your product (the brand, your name) that makes it stand out from others in the field.