Migrations are where optimistic promises do the most damage. Here is the honest version, based on sites we have actually moved.
What moves across
Your text and images move — that is the substance, and it survives any platform change. Your domain moves: it is repointed with a DNS record, and the certificate is issued on the new side. Your structure — sections, categories, the shape of the site — can be rebuilt as it was, because the engine is flexible about hierarchy.
What does not move by itself
Content is transferred by hand or by a studio. There is no universal importer that swallows an arbitrary site, and any platform claiming otherwise is describing a narrow special case. For a site of a few dozen pages this is an evening of work; for a library of hundreds it is a project, and worth pricing before starting.
Custom code from the old site — a plugin someone wrote, a bespoke calculator — does not come along. It has to be rebuilt or dropped, and honestly, most of it turns out to be droppable.
The part that decides whether the move hurts: your old addresses
If your pages change addresses and the old ones simply die, you throw away whatever search visibility they had. The fix is unglamorous and non-negotiable: every old address gets a permanent redirect to its new counterpart. Plan this before the switch, page by page, not after traffic drops.
Where a page has no counterpart — content you decided not to bring — send it to the closest relevant section rather than the home page. A redirect to the front page is a polite way of losing the visitor.
What you should expect afterwards
A short dip is normal while search engines re-crawl and re-associate addresses. It resolves. What does not resolve by itself is a migration done without redirects — that is a permanent loss, and no amount of later optimization buys it back.
Doing it with help
Migration is exactly the kind of work partner studios take on: the technical side, the redirect map, and the content transfer. Their rates are on the partner page. If you are moving a small site yourself, the sequence is simple — rebuild the structure, move the content, map the redirects, then switch the domain. In that order.