Hi @AmyLFrazer, welcome to the community!
From your explanation, it sounds like you have two completely separate Shopify sites, am I correct? Typically, you’ll want to connect one Klaviyo account to one Shopify store - so that the customers, behavior, and order history are properly unique to both stores for Shopify and Klaviyo. You can switch between the two accounts with the same Klaviyo login, but they are two distinct Klaviyo Accounts so you can setup your Welcome Series for each one separately. Depending on your Klaviyo plan size, you can contact Klaviyo to see if they can combine the two accounts into one invoice for billing purposes.
See this thread for more explanation:
However, if they are on the same Shopify Store (but different experiences by the user type in Shopify), you can have two separate Lists - one for your retail customers, and one for your wholesale one. And each can trigger a separate Welcome Series Flow depending on which List they joined in the same Klaviyo Account. This only works if your Retail and Wholesale customers both access your store in the same Shopify Account (and their orders are in the same Shopify store).