It will not look any different to a customer.
The customer will still select from the shipping profiles you have created in Squarespace. This doesn’t change. After they have placed their order, their order details will be sent to Shipstation (or whichever shipping extension you use) so that you can print a shipping label and optionally a packing slip.
@SC2023 - Paul's answer above is spot on. To elaborate further, I always describe shipping on Squarespace as having two sides to an equation:
On the customer side, you have whatever rates you set in Squarespace. This is what your customers are charged for shipping.
On the merchant side, you have whatever rates you're charged by carriers. Using a shipping extension such as ShipStation can help you get better rates and streamline your fulfillment process.
The two are independent of one another and depending on your goals you'll want to either have these two sides net out to zero or bake in a little profit, either by charging your customers more (not ideal) or paying less to ship than your customers are charged.
The only shipping option on Squarespace that would show variable rates based on package size and destination zip code is Carrier Calculated Shipping. Just keep in mind that this controls what customers are charged NOT what merchants pay.
Conversely, a shipping extension controls what merchants are charged NOT what customers pay. So even if you use carrier-calculated rates, a shipping extension can still be really helpful.
Hope this helps explain a bit more how this works!