What are they? I see these words a lot and have no clue what people mean when they say something about a wheel pet or a tegged pet.

Wheel pets: During festivals (such as the Week of Love festival going on right now), there is a wheel you can spin. The top prizes you can get from those are the wheel pets, special pets obtainable only from these wheels. On the wheel page it shows you the pets you could possibly win. However, these pets are very rare and are therefore very valuable. Have you managed to get any wheel tickets or have you visited the wheel yet?

Tagged pets: Any pet that has a purple "tag" on its profile page (if you scroll down) indicating that it is exclusive. Any special pet (not offspring or generated), like a themed pet, will have this if it is first generation (so offspring of any kind cannot be tagged). Wheel pets count as tagged, and other festival pets too.
Take this girl for example:

I got her from a wheel spin. On her profile page you will see the words "Thunderstorm Griffi" in purple.

Or this Hot-Cross Qitari:

I caught her using traps in the festival zone during a festival a while ago. Festival pets like her can be found in the festival zone and are much more common than wheel pets like the Thunderstorm Griffi above.

Ah-haaaa! Thanks so much for the explanation. Yes I've both visited and spun the wheel. Haven't been able to use the "Spin the Wheel (Lucky)" button yet. I got an Acumen Philtre and a Magical Pie.

Isn't a Wheel/tagged pet also a themed pet?

Oh, a Magical Pie? That's better than what I usually get XD The wheel can be very disappointing; you might hear people call it the Wheel of Broken Dreams, lol.
Yes, they are themed.

Yes, you can consider a wheel pet and/or a tagged pet a themed pet. :)

Any pet that has a purple text with a certain word/words associated with the species is considered a themed pet.

_{woops, Alicia answered p quick aha}

@Aliciahou: Really? I thought the pie was worthless until I read what it did. Now that I know what it does its not so useless, but I still dunno what to do with it... I like nurturing my pets and getting scales so... ^_^ I think I'm going to hold onto it for a while though. What do you usually get?

@Flute: No worries. If a wheel pet is a tagged pet and its also a themed pet, why do people talk as they are three different things? Its very confusing.

Well, it gets pretty useful if you're going to do a breeding project. Considering it takes somewhere around a month for an eggling to grow up, magical pies (6-day boosts) are pretty useful.
Even if you don't want to use it, you can sell it for quite a bit of gold. Right now they're going for about 75k-80k gold. Wheel tickets are going for 70k-75k gold, and a philter of acumen goes for 20k (though I feel like they're usually less). A lesser philter of acumen would go for about 500 gold, and if you sold the 2 valentines that would come with it, you might end up with 10k worth. So a magical pie isn't bad at all.
I usually get snare traps and lesser philters. I've kind of given up on the wheel now.

And if you don't mind, I'll answer the question you asked Flute: a tagged pet is not necessarily a wheel pet, so only say wheel pet if it was originally obtained straight from the wheel. Themed pets refers to tagged, but can sometimes refer to offspring of tagged as well (which would have the same color scheme as the parents if it's purebred, but is not tagged as it is an offspring).

Huh... When you say it like that you're right, it really is pretty useful.

And nope, not a problem with you answering. OK, that makes sense, though I didn't know that themed/tagged offspring aren't tagged. I wonder why that is? Anyway thank you both for answering my questions. You and flute were great helps! <3

They're no longer that special because you can breed however many you want. Tagged pets are the originals, and can only be caught or won; otherwise they would lose their value. If you look in the advanced search, there are usually about 200-300 of each tagged pet (unless it's a wheel pet). Any more would make them basically worthless.