Of course you have to register with the new address. Remember the purpose is to keep track of where you are. Even if you don't have a rental agreement officially, they can accompany you to the PSB with some kind of letter stating that you are staying with them.

if staying in hotel, make sure you get a fapio with date booked in / out incase they didn't register you, as they might deny it afterwards to cover thier own ass

"When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean - neither more nor less."
"The question is," said Alice, "whether you can make words mean so many different things."

Through the Looking Glass (PSB edition)

Is this the same with a tourist visa?

ALL foreign resident must register with the police (PSB).

Same for tourists. Every time you move to a new place, from within or from outside of China, even if it's only for a couple of days, you are required by Chinese law to register at the nearest police station.

I like many lived here for years at the same place and never reported each time I left. We are seeing increased focus on the rule of law, Chinese law. In the past, they did not seem to care much about foreigners doing these so-called "monkey" shows, entertainment and acting or tourists taking temporary teaching jobs. Now they check more. Enforcement and interpretion of the rules does vary in from place to place. I too have an "understanding" about when to report travel with my local police station. Its easier to be safe, in this case, than sorry. You should note that this registration form is sometimes needed for other procedures such as work permits and can be asked for when you enter China.

Are they giving tourists with visitor visas a hassle when they first come to China?

tourists with visa, nope. people with tourist visa who then try to change it to student or other visa yes.

www.kmcrj.com/xuzhi/xuzhiid.aspx?id=69

Unfortunately I could not open the English website

重要提示：

1．按照我国法律规定,如果您在出租房、居民家中投宿,须于抵达后24小时内到住地公安派出所办理住宿申报手续(住旅店的由旅店代为申报)。

2．如果您居留证件上的项目内容(姓名、居留事由、护照号码、偕行人等)发生变更,须于变更后10日内到我处办理新的居留许可。

3．您的居留许可期满后如需继续在昆居留,须于期满30日前办理新的居留许可。