The first part of the sync error message means exactly what it says - your iPhone can only be associated with a single iTunes library. The second half is tricky for people that are analytical, but for most users it's meant to make them want to back up their phone before they
Regardless of how you choose to copy your content (sync manually or automatic) it maintains a connection to a single library to which is is allowed to copy music/films/apps etc to and from, and where backups/restores etc can be made. Unless you know exactly what was synced - you could be inadvertently erasing some content hence the scary general error message.
If you introduce your iPhone to a new iTunes library, then it can remove any content that is associated with the previous one. Assuming you still have access to the old one you can copy the files from one computer to another to enable you to sync them back again after, or you can transfer the purchases to the new iTunes library assuming it has been authorised using the same Apple ID. This is an attempt to limit unauthorised copying of music and other content etc, otherwise you could happily take your phone or iPod around to all your friends laptops and merrily copy all their stuff onto your device, where you could then happily sync it back to your iTunes library at home.
Other phone content, like emails, contacts, settings should remain unaffected, as these are not held within the iTunes library (even if you have set iTunes to be the sync mechanism for putting them on your phone, they belong outside of the library.
Rule of thumb: if the original iTunes copied the content on in the first place, it will be removed. It won't just wipe the whole phone, just what came from iTunes.