In general, for SEO and management purposes, I would try to keep yourself to one website. That way people will not confuse the websites if they search for your business. The Shopify app for Wix does allow you to run a store. It is a really basic Ecommerce option, allowing you to sell products, accept payments, track customers, and ship orders. However, the app is not nearly as powerful as Shopify’s traditional ecommerce options, and you cannot add features as you grow, as you can by upgrading traditional Shopify plans. There are no store reporting features of any kind. Also, you cannot use any of Shopify’s third-party apps, which are what give you a lot of important functionality, like real-time shipping quotes. There is no abandoned cart saver either.
In other words, it really depends on what you are trying to do. If you just want to sell some products every once-in-awhile, the app will probably work fine. If you want to sell a lot of products, I would go with Shopify’s traditional option.
Hope that helps!