A product designer theoretically would be more focused on overall user experience and how the product meet the business goals and user context scenarios. An interaction designer would be more focused on distinct sets of interaction within a product.
The skill sets are basically the same, but the distinction is important at the organization level, and points to whether the designer has ownership of the product, or of specified interactions. In a larger organization, a product designer may be concerned with personas, user context, consistency, branding, but not with specifics, where the interaction designer would deal with the specific designs. Overall, the skill sets should be almost identical.
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Answer:
A product designer theoretically would be more focused on overall user experience and how the product meet the business goals and user context scenarios. An interaction designer would be more focused on distinct sets of interaction within a product.
The skill sets are basically the same, but the distinction is important at the organization level, and points to whether the designer has ownership of the product, or of specified interactions. In a larger organization, a product designer may be concerned with personas, user context, consistency, branding, but not with specifics, where the interaction designer would deal with the specific designs. Overall, the skill sets should be almost identical.