Both can be up to 30V and 10A?
Yes, that would apply to each sets of contacts.
BTW - What everybody is saying is true with regular mechanical switches too. i.e. You can use a regular light switch rated for 120/240VAC at 15Amps to switch on & off your Arduino or a little LED, etc.
The coil voltage (and current) is a strict rating... A 5V relay will probably burn-up if you run 12V through it. If the coil is designed for AC, it will usually work with DC, but a coil designed for DC may not work properly with AC. (The specs should tell you.)
With electronics (Arduino, etc.) we are almost always activating the relay with DC. In some "industrial" or "electrical" applications we may have AC through the coil. I've got 12VAC coil relay on a fan relay in my home furnace, and I used a 120VAC coil relay to turn-on the lights in my girlfriend's garage when the garage-door opener is activated.
Solid state relays are a bit different. The input-side usually has a wider voltage range (maybe between 5 and 12V) and the control/output side is more strict/limited. Occasionally, there is no current limiting on the input-LED, so you can choose an appropriate resistor and control it with any voltage of your choice. Almost all solid state relays are DC controlled.
Solid state relays my switch DC only or AC only. Most AC solid state relays use TRAICS and they will lock-on with DC and won't shut off. Many 120V or 240V AC relays won't switch low voltages.