The two jobs are different. A plumber diagnoses and clears the cause - a clog, a broken line, tree roots. A restoration company handles the aftermath: the Category 3 black water, the porous materials it soaked, and the decontamination that makes the space safe again. A serious backup usually needs both.
Speed and certification are what to look for. Sewage is a health hazard that worsens by the hour and can grow mold within a day or two, so a 24/7 crew with IICRC training, proper PPE, and antimicrobial treatment is who you want - not a general cleaner.