I thought we called them ""trial lawyers."
Actually, the term "trial lawyers" also covers those who defend the deep-pockets corporations from these frivolous suits. The plaintiff's attorneys are the ones who actually file them -- and work on a contigency basis. IOW, if the client doesn't win, they don't get much of anything, but if the client wins, they get 33-40% of the amount awarded. But, for the most part, defense attorneys work for set fees or billable hours.
You are a "trial lawyer" if you go to court. "Plaintiff's attorneys DO the suing. Other attorneys are there to defend their client, who is being sued.