Do people know what is being put on the space, or is it private?
It depends. Most hosting companies leave their clients' space alone unless there is reason to investigate: a complaint by a third party, sudden large increases in CPU usage or outgoing email traffic, and so forth. A bit like what you do in your apartment: landlords don't have cause to investigate most times, unless someone else complains about lots of noise, traffic, or what have you. Monitoring clients' web space would not only be resource intensive, but it could actually cause some people to go elsewhere, and not just because they were doing anything offensive. It also, legally (and in a limited way), introduces the concept of 'plausible deniability': if a host doesn't monitor their clients' content and some client publishes copyrighted materials, then the web host is only held legally responsible if they don't either have the relevant files removed or terminate the account, whatever is specified in their TOS / AUP.
Just like different apartments offer different prices, it's the same with webhosting?
Yes, and no. Long answer, sorry
You can rent apartments (or rooms in a house) through many different people, and different apartments with different amenities will have different prices. The analogy starts to break down here a bit, though. With apartments, what city you live in and what neighborhood in that city can afffect price. With web hosts, it's not always the neighborhood (ie, what datacenter the servers are located in, or even which datacenter in which city). Different web hosts run their businesses differently, depending on their individual business plans. There are some web hosts that offer large amounts of disk space and bandwidth, and charge very little for them. There are others that may offer the same amount of disk space and bandwidth, but charge more - perhaps much more. It all falls down to some of the intangibles: for example, does the host both give and take away? One example of this is hosts who offer unlimited bandwidth, but then in the ultra-fine print they say that if you go over a certain amount of bandwidth usage your account will be terminated. Another example might be a host that gives large amounts of disk space and bandwidth, but the servers are very slow and there may be more downtime. Unfortunately, unlike renting an apartment, you can't always tell what is a "good" neighborhood and what is a "bad" neighborhood, in web hosting. It isn't always the same even when the servers are located in the same datacenter.