Gritty players - I am fairly certain that gritty refers to Spirit.
Working hard players - i suppose its determined? - I always assumed that working hard also referred to Spirit, but I am not 100% sure of that. And your thought on it being related to Determined may also be accurate. That's something I had never thought about before so can neither confirm nor deny it.
Mobile players - Skating ability.
smart players - how can i know is he smart player? - I'm actually not sure on this one.
The following is all personal opinion based on having played the game for the last year and a half. There is really no right or wrong way to think about offensive and defensive tactics other than ensuring that your players fit those tactics. I would assume that it would be beneficial to pick offensive and defensive tactics that require the same attributes, but it really is just a matter of preference (which is also part of the fun of a manager game, specifically this one, in that you can set your team up however you want it). I don't think certain tactics work better than others on their own. I have seen many teams have success with different tactics, but again, I think the effectiveness of the tactic really relies on getting players who fit your style.
Playing "very offensive" is based on your team focus. I would assume you have your team focus tactic (when tied) set to Very Offensive. If you want a more balanced game, try setting it to Normal. Try different settings and see what works best.
Two things I think are extremely important. Again, these are personal opinion and maybe not shared among all managers, but just to give a certain perspective.
1. Set your team up the way you want it set up. It's much more fun that way. There is no right or wrong answer when it comes to which tactic works best. To use radical examples, maybe based more on history than current day, if you are a fan of the Big Bad Bruins, you might want to set up your team with big, gritty, physical players and maybe play a Crash the Net style. If you like the Flyers, maybe play a similar style and a bit dirty. Devils fan, try the Trap defense. Kings fan, use Possession. Etc... Then once you pick your tactics, go out and get players who fit your scheme.
2. Test things out until your team functions as expected. Don't be afraid to lose a few games. The most fun I've had playing this game was in the first season when I had no idea about anything and just tested different tactics, team focus, line focuses, line combinations, the list goes on. I was a bit anxious as well and wanted to figure it all out relatively quickly, but thinking back, the journey was much more fun than the destination. Even after 8 seasons, I still like trying out changes here and there to see how they work.
Hope that offers some helpful insight.