An ebook reader is designed specifically for reading ebooks and not a great deal else. However, you can also read ebooks on a tablet computer, which will let you play games, browse the internet and send emails.
Whilst it isn't wildly inaccurate to suggest that tablet computers are like standard computers without the keyboard, it doesn't quite convey the full story. The fact is that most of the main tablet manufacturers have made a big effort to provide an easy to use interface for their tablets.
E-Reader or Tablet Computer? It's hardly surprising that many people get tablet computers and e-readers mixed up. After all, you can use your tablet computer to read e-books if you like (among other things) - and companies like Amazon and Barnes and Noble market both e-readers and tablet computers under the same brand name - the Kindle and the Nook respectively.
A colleague asked me to weigh in on the difference between eReaders and tablets. She's considering buying one or the other, but is confused by the similarities between the two. Tablets like the Google Nexus 7 or iPad mini are my own preference.