The opening of T2 is a deliberate play on audience expectations (even if they spoiled it pre-release) drawn from the first film. T1's opening makes a very big deal out of how mechanical and oblivious to danger the T800 is, and how fragile and human Kyle Reese. The former methodically accomplishes each step towards finding Sarah Conner, while Reese fumbles.
T2, on the other hand, deliberately humanises the T1000 a lot more than the T800. Until the T800 properly meets up with John, the only thing you ever hear him say is "I need your clothes, your boots, and your motorcycle", mirroring the mechanical, methodical hunter approach of the T800 from the first film. Meanwhile you see the T1000 meet people, ask questions, and interact with the public, and generally talk like a normal person.