Yes, Microsoft Exchange Server is a peice of software. It's a common email server side software. It hosts the mailboxes that are created. There are several different "flavors" of this software all priced differently. Lotus Notes, iMail and MANY others are alternatives available.
Yes, you are correct, to a point. If a company installed the standard edition of exchange, (don't know what network admin would with 10k users) you have a limit on database storage. This is a software limit, not hardware. The enterprise edition of Exchange is either not limited or has some astronomical size. I can't remember exact details right now, Microsoft keeps changing the rules. For an organization your size, you are likely running the enterprise revision.
Server hard drives are VERY different from pc drives. High end servers, like what you would use to host Exchange, usually use 15,000 RPM SCSI drives. Email servers are very intensive with their hard drive writes, called Disk IO. There is a lot of this done during normal operation. Currently, the biggest drive I can get is a 15k RPM 450Gig SCSI hard disk but the price is like $800 per drive. For a raid 5 setup, you need at least 3 drives.
http://en.wikipedia.org/wiki/RAID
If your company is running a RAID 10, you need double the amount of drives than normal.
You also have to take into account how you utilize your disk space. If something was purchased before you got so big, it might not be "right sized" for the job at hand. Sometimes, just getting gear in to fill your needs can be VERY expensive. Sometimes CIO's will approve the cost of the software one year, and the cost of new hardware another.
The 2TB drive Slowpoke mentioned is a SATA drive. Those spin at 7200RPMs. Not recommended for an email server. Not nearly fast enough. Keep in mind the 10k users here again...
The difference, is always SPEED!