Intellectual property remains whole for the author(s).

However, the author may choose to transfer their property rights via contracts or using licences which aim at a wider circulation, with a Creative Commons type licence in which the author(s) define any authorised uses themselves.

"When uploading their texts to an open archive, authors and afferent right owners concede to all users a worldwide, free and irrevocable right to access the work. Uploading also entails a licence authorising them to copy, use, distribute, share and show the work in public, and to create and circulate derived works, on any digital media and for any responsible purpose, provided the author is duly mentioned (usual collective rules still apply for enforcement of proper attribution to the author and responsible use of the published work, as now), as well as a right to print a small number of copies for their personal use."  (Berlin Declaration on open access)

Yes, in accordance with copyright, i.e. as a citation, mentioning the author and the reference, and for the copier's private use.

Users are indeed submitted to the usual use regulations for scientific publications.

Moreover, the more visible a document becomes on the web, the more renowned its author. Then it becomes trickier to plagiarise it.

The author, by uploading their text, authorise users to copy and show their work, for research and lecturing purposes.

This conveyance is free of charge and non exclusive. In turn the open archive commits to respecting the paternity right (the author's name and references) and the work's integrity right.

It also warrants database permanence and data durability.

Therefore, in order to facilitate long term document protection and online citing, it is recommended not to request withdrawal of a self-archived publication.

However, some open archives do make withdrawal possible.

What is the difference legally between publishing on one's personal website and uploading to an open archive?

As opposed to an ordinary website, the open archive commits to mentioning the author's name and to guarantee the integrity of the work, and ensure long-term access to it.