In other words, one song might fit such a description. However, it's very rare that a band writes all their songs to fit within a small sub-genre of music. I would say that Pennywise is the only band that comes to mind that does that.
The Offspring, to me, writes songs that can fit under many "genres". They've used metal, rock, punk, rap, reggae, ska, acoustic, pop, etc. If I had to name one main genre to describe them to someone who hadn't heard them, though, I would call the band pop-punk. "Pop" because they are/were very popular and write songs that are very suited for the radio (even a couple songs on the first two albums could've hit the radio had they had promotion). "Punk" because of their tendency to stick to a 3 chord structure, fast driven song tempos, and a lean toward anti-establishment/conformist lyrics.
But as a musician myself, I've always had a hard time with the concept of trying to categorize music. For instance, I think it's hilarious that any music whose instrumentation solely consists of string and wind instruments is automatically considered "classical" music... sorry, everyone, but the classical era ended a LONG time ago. :P
Edit: I'd like to add that I don't even think more than a couple Offspring songs really fit into what I consider "Skate Punk". I generally agree with the definition on Wikipedia: "Skate punk typically uses four note basslines, surf-like drums, and fast, Ramones-style guitar. Mostly played on the upbeat instead of the downbeat, skatecore is known for emulating the "feel" of skating... Skate punk utilizes quick uptempo "jumps" of silence at the end of the measure to emphasize the start of the riff." However, like I said before, I dislike categorizing music. I wouldn't argue with someone who considered their music to be skate punk, because music genres just can not have one divinely truthful definition.