It seems there is a bit of confusion over these four terms, which are all thrown around a lot, particularly here in Australia where DSL-based connections are generally the best and fastest options available for broadband-speed internet. They also have reasonably wide availability.
First, what is DSL? DSL stands for Digital Subscriber Line, and it's a last-mile Internet technology (ie. between the telephone exchange / central office and the home) that allows you to send digital information over the phone line at a much higher bit rate than a dial-up modem, which is the other option for transmitting data over the phone line.
DSL does this by operating at a higher frequency than regular phone signals (devices operating on the normal phone spectrum such as phones, fax machines and dial-up modems are known as "POTS" devices, for Plain Old Telephone Service). This means that with the use of filtering technology, POTS services can run uninterrupted on the same line at the same time as DSL. You can read more about how exactly DSL achieves this at the Wikipedia article on DSL.
Most Australian ISPs are marketing "broadband internet" as internet that is faster and does not "tie up your phone line" while you're using it (as opposed to dial-up). Most of the time, they are talking about ADSL. This stands for Asynchronous DSL, and it essentially means that your upload speed is not as fast as your download speed (although technically, it would be possible to have an ADSL plan with faster upload speed than download speed, this is practically useless for 95% of users).
Recently (ie. over 2005), Australian ISPs other than Telstra (the owner of all the copper wiring and telephone exchanges / central offices) have begun installing their own DSLAMs in exchanges. These have been marketed in quite a confusing way. DSLAM stands for DSL Access Multiplexer, and a DSLAM must be installed in the telephone exchange to multiplex (combine) communications between DSL users connected to that exchange, and transport them to the ISPs high-bandwidth backbone. To clarify that, it performs two major functions: it acts as a DSL modem to convert the signals received over the phone lines into data that other transmission hardware can understand, and it combines all the data being transmitted over all those lines into one big stream that can be transported over a single line (typically a high-bandwidth fiber optic line that is connected to the ISPs backbone, and from there, to the server that the user was trying to reach).
This means two things: first, that Telstra would have had to install DSLAMs into all exchanges to offer DSL in the first place - and that other ISPs, starting with iiNet, were doing nothing "original" by installing DSLAMs, and second, that people who say that DSL is better than cable because you get your own line instead of sharing bandwidth with your neighbours are wrong. While the problem is not as bad, all people hooked up to one DSLAM (typically around 50) are limited by the bandwidth of the fiber optic line connected to the backbone. However (hypothesizing here), most fiber optic lines operate at gigabit speeds and higher, so that still leaves 20 Mbps for each of the 50 users on a DSLAM, assuming full utilization (and no ISP would be able to survive if all users were maxing out their connection constantly). This is in contrast to cable, which frequently leaves users with an equivalent of less than a megabit each if link speeds are maxed out.
Anyway, the reason that ISPs began installing their own DSLAMs is because Telstra artificially limits all ADSL connections that they wholesale or retail to a maximum speed of 1500/256 - that is, 1500 Kbps download, and 256 Kbps upload. The ADSL specification allows up to 8 Mbps (8000 Kbps, more than 5 times Telstra's limit) download and 1 Mbps (roughly 4 times Telstra's limit) upload, so at first, it seems like Telstra are just screwing their customers.
However, there is a good reason for their limit, although it is a little excessive. As the length of the copper line between the home and the exchange increases, the ADSL signal is degraded significantly, such that at any distance over 5 km, ADSL is essentially useless. Telstra will provide ADSL access to any customer within roughly 4.1 km of the nearest exchange (keep in mind that this is the copper line distance, not the direct distance of a straight line between your house and the exchange). This is why most regional customers can't get ADSL. At that distance, connection speeds of approximately up to 3.5 Mbps are possible, but as a lot of the copper lines are of low quality, and most users opt to "self-install" ADSL using microfilters (aka inline filters) rather than a central splitter, line quality can be degraded significantly. Therefore, Telstra offers a maximum speed of 1.5 Mbps so that they can effectively guarantee a 1.5 Mbps sync speed to anyone within the 4.1 km limit. This is best demonstrated by a graph.
At the moment, we're looking at ADSL (blue) and Telstra (red). As you can see, they have a comfortable margin in which to operate. (I'll discuss ADSL2 and 2+ later, but just so you know, READSL stands for "Reach Extended ADSL", and its a fairly self-explanatory idea. It provides ADSL to distant customers, although it is not yet widely available.)
So that's why iiNet's 8 Mbps internet connections seemed so special at the time they were released, despite the fact that all they did was purchase essentially the same hardware as Telstra without installing limiting software on it.
As for ADSL2 and 2+, those are more powerful versions of ADSL, basically. I won't go into the specifics of how they work, but as you can see from the graph, their advantage over ADSL is really only noticeable within 2 km of the telephone exchange. Both retain the 1 Mbps upload speed from vanilla ADSL, but ADSL2 allows up to 12 Mbps downstream, and ADSL2+ 24 Mbps. To operate at those sort of speeds, in addition to living close to the exchange, you'll need to have an ADSL2/2+-compatible DSL modem. Obviously, the ISPs DSLAMs need to be compatible with 2+ as well, currently only iiNet, Adam Internet and Internode have their own DSLAMs, with iiNet having the largest number of them. Currently, all three support ADSL2+ on their networks, but Telstra's DSLAMs don't. Telstra has stated that they will support ADSL2+ in 2006, but I have my doubts as to whether this would happen; surely if they were going to offer a service that is only useful to a tiny percentage of their customer base (those using 2+ speeds and within 2km of the exchange) they would have started by uncapping the regular ADSL connections to 8 Mbps, and they announced that back in March.