"a lawyer whose clients are mostly corporations and the subject of whose primary expertise is corporate (and financial markets and maybe tax) law. Is that not true of Obama?"

No, that is not true of Obama.

He chose to work for a civil rights law firm.
That was a major point in his biography. He could have made more money working for corporate clients, but he chose not to.
Cases he worked on for example related to voter registration (where the ACORN connection comes which was used in attacks in the campaign), funding for minority housing, and defending a whistle-blower.

You can read more details about his rather brief career as a lawyer in this 2007 article in the Chicago Sun Times:

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