Yes and no ~ that needs some elaboration. As always on these pages it is just me talking ~ I may have got things wrong. By way of explaining my use of the words ~ here is my opinion and belief.
Bookbinding is a trade that has developed over the last dozen centuries. A hand bookbinder has mastered the techniques required to make sensibly ~ beautifully ~ bound books ~ Fine Bindings in a great many ways. Experience shows that the best and quickest way to become a bookbinder is to sign on as an apprentice to a master binder. Over the years the skills of the master are shared ~ and a wide experience is developed. Such apprenticeships are few and far between ~ as are the master bookbinders with the necessary skills.
The Institute for Apprenticeships and Technical education suggests two years for initial training [IATE]. I always though it was more like five years to get anywhere near being a reliable fine binder. The Queen's Royal Bindery at Windsor Castle offers occasional apprenticeships ~ think in terms of one or two every few years. Expect to have to search around to find such an opening ~ try using search-words such as 'Heritage'. There are several colleges offering suitable courses of study ~ an excellent way-in to the trade.
I have been at length to explain my definition of a bookbinder, and I would like to reserve the term for those who have really earned their colours. Just as a joiner ~ plumber ~ electrician ~ or bricklayer earns their title ~ which should not be confused with the d-i-y expert who can make a bookshelf ~ mend a fuse ~ or change the washer on a tap. The descriptor of my choice for those without the time-served qualifications is bookcrafter. It is not meant be a denigrating term ~ there is tremendous talent provided by bookcrafters around the World ~ they also have my full respect. The WWW has thousands of tutors offering to share their skills ~ give them a try. Be prepared to spend several happy hours browsing and watching fascinating bookcraft videos.
That leaves bookmaker. Anyone can make a book ~ most people can make very well designed and serviceable books. It takes a bookbinder to make a Fine Binding which is another trade term ~ to be reserved for the output from the true masters of their craft.
The previous paragraph opens another can of worms. What is a book? It makes me sad when I hear the comment (as I often have done) 'That's not a book'. I have stuck my neck out far enough for today ~ more anon ~ perhaps.