Your Price Book is the one catalog. An item or service shows on the store block the moment it is priced, not deleted or archived, and marked to show on the site (the same "Publish on site" switch that controls where else it appears) - and, if you assigned items to specific companies, the site's own company. Nothing about the item is retyped for the website: change the price, the photo or the description in Items and Services and the site picks it up the next time a visitor loads the page.
Say "add a store to my website" in the site's Genaya AI chat, or add the Store section from a page's section picker. Genaya AI adds a grid of everything already marked to sell online; nothing is added or changed in Items and Services itself. Building a new site? Say in the brief that you want to sell online and Genaya AI plans an Order page with the store, the cart and the checkout for you, as long as GenayaPay is set up and at least one item is priced and marked to sell online.
On Dashboard > Settings, turn on Pickup, Delivery, or both, for the site. Pickup needs one pickup location once your organization tracks stock at more than one; Delivery is one flat fee per order, the same for every address - there are no shipping zones or carrier rates yet. A cart of services only (nothing to pick up or ship) needs no fulfilment method at all.
A service never needs stock. A physical item follows the same Track inventory switch and quantities you already set in Items and Services; when it runs out the site marks it out of stock automatically unless you turned on "Continue selling when out of stock".
Publish the site the normal way. Tax follows your organization's default tax on the items marked taxable - there is no separate tax setup for the store.
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