The short answer to this question is - no. Book printing press is not different from a magazine printing press; both books as well as magazines can be and are being printed on the same machine and these can be either sheet-fed offset or web offset printing machines. The choice of machine depends entirely on the printer who will consider the cost-benefit ratio of using a particular machine. In case of a short run job with minimum order quantity, conventional wisdom might suggest that the printer will use a sheet-fed machine to do the printing and for a long run job he will use a web offset machine.
After all sheet-fed machines offer the flexibility of controlling the print run as required but assumptions don't work in cost-benefit analysis. The printer will consider the cost of printing on the basis of factors like operating cost of the machine which includes the manhours of the personnel operating the machine, the cost of paper including wastage (unprinted portions of the sheet), cost of consumables like ink and power among others. In a web offset machine, the printer will optimize and combine several smaller jobs in a single print run where the costs get divided among all the customers whose job orders are combined in the print run.
In the case of book printing, there are several post-printing processes like cutting, folding, stitching, binding and cover binding that need to be completed before a book is ready to be sent to the publisher. In the case of a magazine, the post-printing processes are cutting, folding and pinning in case of the lesser number of pages, or binding in case of a thicker magazine with more pages. Most printers these days are equipped with a range of printing machines to service a cross-section of the market with different price thresholds.