I heard someone say that ethernet connection is vulerable if someone can connect to your LAN, and that the traffic isn't encrypted in the way it might be if you're using WPA wifi encryption. Is this true? And should I stop connecting via ethernet if the connection is not encrypted? I am connected directly to my cable modem.
The answer also depends on the physical aspect of the network configuration.
If your modem or router (or combo) is easily accessible by someone else, it is much easier to eavesdrop through Wifi, although like @VirtualJJ said, the communication is encrypted. Because through the LAN with ethernet protocol the communication can be wide open for anyone to sniff, but the fact is you have to be able to hard connect to the network.
The wifi is more easily accessible, yes, but it is encrypted and through a strong password and perhaps extra care (SSID not broadcasting and limited power on your wireless some it does not reach much further than your appartment) it can become more secure.
BTW, VLAN is a virtual LAN which means that you can group nodes. Usually you would group devices that need access to the same thing (same requirements) such as security devices (access control, alarm, cameras) or sales staff that needs access to a particular server. You basically create different segments independently of the physical portion. (Very useful feature)
Ethernet (802.3) and wireless (802.11) are simply communication protocols. How secure they are depends on configuration. How to configure security for both ethernet and wireless will be out of scope for this answer.
Out of the box, with no security configuration at all it would be easier to eavesdrop on an unencrypted wireless connection since the person eavesdropping doesn't have to plugin to the LAN and can sniff the traffic out of view. (e.g. use strong wireless antenna and sniff traffic from car a few blocks away)
If the wireless connection is secured using WEP or WPA it will be slightly more difficult but almost anyone can learn how to do it with a quick search.
If the wireless connection is secured using at least WPA2 then it would be very difficult so then the LAN would become the next easier option.
Depending on the physical environment we are talking about (i.e. corporate office, coffee shop, hotel business center) it would be easier to sniff traffic on ethernet if no VLANS or other controls are in place on the network over a properly secured WPA2 wireless connection.
If you are using a public ethernet (i.e. LAN drop) or wifi connection this is why it is important to use strong versions of VPN and/or HTTPS to protect your communications since you don't have control of the security of the network.
Wireless networks are always on, and always open to being cracked. That said, WPA2 with a strong passphrase will be very difficult to break. So, for wireless, it really depends on your settings.
Physical ethernet wires are not encrypted, but they have the benefit of being physical: if you can secure the physical ports (and cable modem in your case) so that no one can connect, then that's even better than an encrypted connection (although both would be better).
If you are sharing your space with roommates/family, then you have a tricky situation. If you don't trust who has access to your network, then a strong wifi WPA2 passphrase might be the better solution.