The defintion of "casual" depends on the person reading it and who made that claim about their guild. As does "casual competitive" - the term is meaningless.
I was in guilds that were casual, similar to what you described, but when lack of participation (and inability to finish HSTR back when it was new) made me want to leave and find an even more casual guild because i didn't want to deal with the stress of having to beat my head against the wall to get enough points in HSTR.
And when i was looking for a "smaller guild", I actually found a bigger guild that was just as casual, but everyone did their part. Most everyone got tickets, TW win rate was solid, and TB stars were good. I eventually became an officer in that guild and stuck around for a while. By the time i left, the guild had fallen off a bit, no longer competitive in TW, but still good in TB. Raids were hit or miss.
And I found a different guild that didn't describe themselves as casual, but based on the friend that recruited me, said it was just as casual as my previous guild. And he was right.
So to summarize my long winded answer, don't pay attention to the labels that someone puts on their guild (casual, competitive, relaxed, etc), just look at their results (TW win rate, which raid box are they getting, TB stars) and ask questions of the officers (or whoever is recruiting you). Find out how often they launch raids (hint, 30K tickets means raids launch every 6 days. If it is close to that, you know everyone is getting close to 600 per day). Ask about the stuff that is important to you. And you'll eventually find the right guild for you