The text records a technical difference between Imam Abu Hanifa and his two principal students. For Abu Hanifa, thumma indicates separation in both utterance and legal effect. For the students, the legal effects are successive while the speech remains syntactically connected.
“Separation in wording” allows a later part to function as a distinct utterance. “Succession in legal effect” means that the later consequence is placed after the earlier one. The difference matters when a first effect can change whether a later effect has a subject to act upon.
This is a school-specific analysis of particular formulae, not an automatic ruling for every use of thumma in ordinary speech.