What is your baseline for a "cheap one?"
Having asked that, the bottom-basement priced pointer(harbor freight) are good for a minimum for detecting but they a junk for durability and out of the box performance. Really, they are cheap for a good reason, they break! I thought about buying one when I began. I was gonna buy 2 to get ready for the first one breaking. At $16, I thought it smart at the time. Luckily, I bought the Garretts proPointer, even at the large price difference in cost.
In conclusion,,,yes thay all do the same things generally...for a while.
BTW, you should highly value the warranties and CS reports from these websites. The best PPrs have a 2 year warranty.. If you are simply buying into the detecting hobby at ground zero, I imagine pointers at or above $100 seems like nonsense. My opinion changed quickly.