Significant difference and similarities
Bookshelf speaker is a term that came around when the acoustic suspension speaker came into existence. The AR line of bookshelf speakers, shown on bookshelves in their advertising, were a direct contrast to the speakers others were making like the Bozak, ElectroVoice, and such that were, on the small end, the size of an end table and went up to a wall of sound, 3 feet wide, 4+feet tall and a 20" deep. A statement piece in the room and by this time you needed two of them. So the term Bookshelf Speaker came about to cover this new set of speakers that were 1'x1'x2' and had good bass response because of the acoustic suspension design. Speakers this size and below kept that name.
Enter the early subwoofers and Visonik that made the David speakers. The David (D-50 or some such Visonik model number) speaker system was augmented on the bottom end by the Goliath subwoofer which was made by Miller & Kreisel because they heard the David and decided that a sub would make it a viable full range system for home use. Now the term Sub Satellite Speaker System was born. The satellite would not do bass and needed the help. The bookshelf speaker could do bass and was a stand alone speaker system.
That is generally how things got started and the naming morphed a bit but I kinda stick with the original ideas. Many small speakers today with response down to about 50Hz are sold as stand alone stand mounted speakers but these suffer from lack of bass. That is fine, there is a market for speakers like that at many price ranges, best I heard was a pair of Dynaudios at about $6,000 the pair for a small speaker. These could/should be used with subs but some decide they don't need the bass response, apartment dwellers or WAF reasons, and accept the speaker with its limitations.
Today, I guess a satellite speaker is one designed specifically to be used with a sub. Many HT systems have this. It is hard to say that some of the very small speakers designed to be used with or without a sub are satellites, just limited range small speakers. Newer technology and the market demands have caused this market segment to expand considerably in the past 20 years. Great sounding small speakers that can be but don't need to be augmented with a sub and are generally not used on a bookshelf but on stands.