For buyers contracting authority
Choose 72413000 when the deliverable is a website: a new site, a redesign, or a portal built on a CMS the contracting authority will run afterwards. The visual design, the user experience and the front-end build all land here, and so does the development work needed to make the site function.
The boundary that trips authorities is 72415000, site operation and hosting. Design and build the site under 72413000; run, host and keep it online under 72415000. Many contracts bundle both, so set the primary CPV code by whichever dominates the statement of work, then list the other as a secondary code.
Two more neighbours matter. If the contract's main output is a custom application rather than a website, that is software development (72262000). If the work is broader internet build beyond the site itself, Internet development services (72420000) fits better. Reserve 72413000 for the case where a website, with its design and front-end, is what gets delivered and signed off.