What the export includes
By default you get one standalone HTML file with the page structure, all styles and the images baked in. One file is the whole work, and anyone can open it.
You can also export a project bundle: HTML and images packed separately in a ZIP, ready to deploy to your own server.
Export vs. a published link
Publishing hosts the page on inksss: you get a link and see visitor stats here. Export hands the files to you to keep. They do not conflict; many people publish first and export a copy for archiving.
What you can do after exporting
Keep an archive; deploy to your own server or any static host; hand the source to a colleague. If you want to keep editing, upload the HTML back into inksss.
Does membership expiry affect export?
Your work is never deleted when a membership expires. Export availability follows your account entitlements at the time; see the pricing page for details.