In common usage, Serial often refers to WAN communications. Also in common usage, Ethernet refers to the Ethernet family of protocols, often used for LAN communications, but today, they're often also used for Metro and WAN connections too.
As Ethernet is also serial in its transmission, to compare differences you would need to compare specific serial protocols, which there are many, with specific Ethernet protocols, of which there are also many.
Generally "Serial" protocols often only deal with L1 specifications, their L2 protocols being provided by another family of protocols while Ethernet protocols provide for both L1 and L2 specifications.
Also "Serial" protocol often have specifications dealing with Telecom issue, "ring", off/on-hook, clear to send or receive, etc.
BTW, if you're wondering why there are so many protocols, it's because they differ in the media and speeds they support, both of which evolve over time. For example, Ganesh mentions both RS232 and V35. If I remember correctly, RS232 is supposed to support 9.6 Kbps at 15m while V35 supports higher speeds, although I not sure to what distance.
Copper Ethernet, as I'm sure you're aware can be found supporting 10, 100, 1,000, 2,500, 5,000 and even 10,000 Mbps. (The last, though, I don't believe to 100m.)
