Dear Victory
Concern also means care. The sentence means some people care about, think about the welfare of the entire organisation whereas some try to get away by doing as little as possible.
Eg X is in charge of buying paper for the office, and he only sticks to his job ie buys paper. He doesn't care about anything else
outside his job such as
1)company progress (sales, profits, brand visibility)
2)company activities (workshops, participation in trade fairs, sales promotions)
He doesn't offer suggestions to improve company performance or even the processes in his own job such as
1)how he can get better quality paper at better prices
2)how he can shorten the paper procurement process or make it more effective/secure etc
X is the type of person mentioned in the 1st part of your sentence, by now it must be obvious what the other kind is.
Best wishes
Rakhee, Bangalore