The second type of lawyer would instead come up with whatever legal reasoning was necessary to please the client, stretching case law and legal analysis in such as way as to justify what the client wanted to do. This type of lawyer had no integrity. His task, as he saw it, was to provide legal cover for his client in case things went the wrong way.
Stereotypes would suggest that's the more common type.
I'm actually pretty curious about how attorneys should balance this. The idea that everyone deserves the strongest possible defense (which I mostly agree with) suggests that being the second type of attorney doesn't require a lack of integrity.
Presumably our adversarial legal, political, and economic systems are designed to function well even when people are acting like total dickheads. I think there's some truth to it, actually