there are 3 recent (modern) mustang chassis.
Fox body is the 79-93 chassis. There were some minor changes made in the middle of that span but they're all basically the same chassis. Notchback, hatchback, 4-eyed-pride and LX are all basically synonyms describing certain aspects of various Fox body models.
SN95 (also fox-4) references all stangs from 1994-2004. This family breaks up into a few sub-classes: 94-95 are the truest SN95's and are best referred to as SN95. 96-98 had minor modifications and the new 4.6L engine and are called Sn95's, turds, jelly beans, and any number of derogatory terms. 99-04 are called new-edge and that references the significant restyling of the body that was done. 99 was also a landmark year for base hp. SN95 chassis cars share about 30% of design and componentry with earlier Fox body cars.
S197 is a completely new car. The only thing it has in common with the last car really is the name and some drivetrain pieces. This is the era of the 3v mustang. All mustang from 05-present are S197 chassis.