This is more a question of definitions, and I disagree with the 2 current answers.
Publish is a more general word than print, but the 2 words are not even really related.
To publish a book means to have it printed and to make it available to the public (which could be for free, or for sale).
Printing is only related to printed press, so note that publishing an article in a scientific journal may require no printing.
You can publish a game on steam, which requires no printing.
So publishing something really means to "ship" it. Publishing means saying "this is the final (or maybe just the first) version, and it's ready for you guys to read". And to make it available to the world. Publishing something means it's no longer your private information/document/product/program etc - it is available for purchase/free.
Note that the definition require that the content be made "public". Some may interpret this to mean that because only students at your university can buy it, it is not really public, so you can't use the word "publish". This is not accurate. Even in such a case the book is considered published and is considered publicly available to the whole world because anyone in the world could become a student of your university and could then purchase the book. Note that some scientific journal articles which "publish" their journals, only sell their articles selectively to users who have a specific subscription from a research body or a university. These are still considered published, because anyone could get access to such a subscription and would then be able to purchase the articles.
Regarding the specific details of your situation: your book would be considered published. Since you would have a finished book ready for print, you could consider contacting other publishers and getting a deal for them to publish it further, nationwide or worldwide.
So yes the book would be published, just as when I hit "Post your answer" I am publishing my answer. The difference is that I am publishing an answer, while you are publishing a book to your university book shop. So congratulations and please consider contacting other publishers and expanding it further.