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The method I've seen most often is to send the data from the website to your in-house customer management software. That software can print labels.
Most shopping carts assume your business already has a suite of software that it can't live without, and it doesn't seek to replace that, it just becomes an additional "sales center." The better carts can output their activity in comma-delimited datafiles for your main db to slurp up and process.
Maybe that's the "old 90's way" but in my experience, that's what most people are doing. Perhaps the movement is towards having one software company stock your office PCs with business software, and your web server with ecommerce server, and the whole thing just grooves together like one big happy family. And I'm sure we all have an idea of which giant software corporation wants to do that for all of us :-P