They are all kinds of server platforms both from a hardware and software perspective.
A mainframe is a server. These tend to be extremely expensive - Some companies spend millions on a single mainframe before they even get billed for mandatory service agreements! These are what some people call "big iron" and IBM is one of just a few vendors still selling mainframes. mainframes are big powerful machines, typically running proprietary processors and operating systems - IBM mainframes run the IBM Z/OS and also can run Linux. The beaty of the mainframe is that it is the closest you will get to 100% uptime from any server type. mainframes do not run as a single server. Each mainframe is capable of running many VM's (Virtual Machines). A single mainframe can literally run thousands of individual server instances in these virtual states. You can also deploy a new server in this VM state in under 90 seconds. Pretty impressive... but very expensive. But also one of the most secure combinations of hardware and OS anywhere... Ironically, a mainframe had never been truely hacked until they started running linux on them.... Don't believe everything you see in the movies..
Intel platform machines can also be servers. These typically run a Microsoft or Linux server OS and Zeon processors... AMD Opterons also fall into this class of server architecture as well. The advantage of the Intel/AMD platform is that the up front costs can be cheap. The disadvantage's are that they have a high cost of ownership ie; expensive to manage, and that they essentially have the worst uptime of any server architecture/OS combination out there, whether they run Linux or Windows. Apps like VMWare allow us to now run VM's on INtel and AMD. So instead of buying multiple server boxes for multiple uses, we now get the most utilization out of our servers by running multiple vm' (virtual servers on a single box - easier management, less power consumption....
There are also RISC based servers. IBM power pc processors are RISC based and they have special variants for server use. IBM's P-series servers, and I believe i-series (as400) , run RISC based as well SUN, and several other brands like HP, etc.... The advantage of RISC paltform servers is that they tend to offer the absolute highest performance of any platform out there. They are the best performers in handling web applications under heavy load. They can run 64 bit linux - Have for some time - and various types of UNIX. IBM's version of UNIX is AIX. The i-series tends to be very mainframe-like in that it doesn't offer the performance of the P-series, but offers the stability of a small mainframe(but cheaper up front) with excellent management features - lowering cost. You can also do virtualized environments in machines with this architecture as well.
As far as uptime and reliability is concerned... here is where they rank.. using IBM model lines as reference points.
#1 - mainframe -Z-series/Sys390
#2 - I-Series (AS-400)
#3 - RISC - P-series
#4 - CISC - INTEL/AMD
From a cost of entry standpoint here are the rough rankings...
#1 - CISC -Intel/AMD
#2 - RISC - Pseries
#3 - i-Series/as400 -Though these can be close to the RISC based systems in price at time.
#4 - Mainframe.
So there are many different server paltforms and combinations of that hardware with various operating environments to achieve various affect. The size of a customer and the number of users/apps they need to support can dictate/help dictate what platform they choose.
A small/medium business wouldn't buy a mainframe, though they could rent the use of a few virtual machine states on one from IBM, Fujitsu, etc.... Small and medium business's typically are INTEL/AMD, and some medium sized businesses run RISC boxes.
Large companies tend to have a bit of everything it seems and the very large corporations invest heavily in the mainframes as their main backend for their over-all infrastructure.
Anyway i digress.....hopw that helps.