South Africa won the second Test by an innings and 62 runs inside three days on Sunday, adding to their first Test victory in less than two days in Cape Town.
"We've come a long way since the start of the one-day series against England," Smith told reporters. South Africa won that series after losing a home Test series to England for the first time in 40 years.
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South Africa's win was sealed by the bristling fast bowling of Monde Zondeki, who took a career-best six for 39 in only his second Test.
"I knew I would take wickets if I put my back into it, and it was important to take early wickets," Zondeki told reporters.
Zimbabwe captain Tatenda Taibu was asked whether his team had progressed or regressed in the series.
"We haven't gone anywhere, we didn't move, this tour has shown us exactly where we are," Taibu said.