Omni-channel integration means the screen, the app, the site and the store work from the same data, so a customer moving between them does not start over. The screen shows what is actually in stock in this store; the basket started on the phone is there at the counter.
The bar is genuinely shared state, not simply being present in several places. Having a website and screens is multi-channel. Having a screen that knows the customer's basket is omni-channel, and the difference is entirely in the plumbing.
The caveat is that most omni-channel programmes fail on identity, not on screens. Recognising the same person across a phone, a browser and a physical store is the hard part, and doing it without a consented login usually means tracking that is legally awkward or technically fragile. The projects that work give the customer a reason to identify themselves (a loyalty account, an order number, a scanned code) rather than trying to infer it.
Start from the one handoff that is worth the most and make it genuinely seamless. A programme that improves six journeys slightly is indistinguishable from no programme.