You should almost always ignore the total number of states (3). It is affected by lots of factors and can change from run to run on the same input spec. Only the number of distinct states (2) really matters.
The more interesting question is why you saw two "B"s!
The model checker does not just visit every reachable state; it also visits every reachable action. Your spec has two reachable states:
...and two reachable actions:
v="A" ---[SetV]---> v="B"
v="B" ---[SetV]---> v="B"
Yes, the second one is indeed a legal action, even though it doesn't change any of the variables! I suspect the second "B" is the result of the second possible action, where v does not change.
To see this in action, add "/\ v' /= v" to the definition of SetV before the PrintT call, thus requiring it to change the value of v. The second "B" should go away.
One final warning: the PrintT calls happen while the model checker is exploring. The model checker promises to explore everything, but it doesn't really promise anything about what order it explores things or how many times it visits them. If you use multiple threads, two different threads might visit the same action in parallel, and you will get duplicated outputs. So while there is a good explanation for the two "B"s in this simple case, you shouldn't necessarily rely on PrintT to behave how you expect it does in a real programming language.
I have this very simple spec
vars == << v >>
Init == v = "A" /\ PrintT("A")
/\ v' = "B"
/\ IF v' = "B" THEN PrintT("B") ELSE TRUE
Spec == Init /\ [SetV]_vars /\ WF_vars(SetV)
If I model check it in TLA Toolbox, I get
1 state found for action Init and 2 states found for action SetV
for a total of 3 states but 2 distinct ones.
The output is also "A", "B", "B". Why two "B"s? Why 2 identical states?
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