The second-generation iPods had different hardware, I believe; you had to buy a "Windows iPod" to connect to a Windows machine, and an "Apple iPod" to sync with an Apple machine. The current generation iPod is multi-platform. The same iPod could be used to sync with either a Windows PC or a Mac.

BUT...the iPod is designed to sync with one machine at a time, anyway. If you synced with Computer 1, and then plugged your iPod into Computer 2, it would prompt you that the iPod is already designated to a different user. You could opt to switch it, designate it for Computer 2, but it would wipe your iPod clean first, and replace the music from Computer 1 with the music from Computer 2.

In fact, it works that way between different user accounts on the same machine, too.

Provided you use iTunes your Windows-formatted iPod can also be used with your Mac, but not vice versa. It worked the same way with Gen2 iPods, one was formatted for Windows, one for Mac - they had identical hardware!