Thumma is also a conjunction, but unlike fa it normally marks an interval or delay between the linked elements.
«ثم: للتراخي»
Thumma denotes succession with delay.
“Zayd arrived thumma Amr”: Amr’s arrival follows with an interval.
“Zayd arrived fa Amr”: Amr’s arrival follows closely.
“Zayd arrived wa Amr”: both arrived, with no specified order.
The three particles are not unrestricted substitutes for one another.