The Inquisition's consultant Theologians in 1616 thought heliocentrism was a heresy, as it lacked evidence and so shouldn't be used to reinterpret scripture.
The Roman Inquisition cited the Theologians, but themselves never called it a heresy, using the words "false, and contrary to scripture".
If they had ruled it to be an actual heresy, Galileo would have been made to abjure in 1616, and heliocentrism could not have been held as a hypothesis, De Revolutionibus would have been banned instead of censored, Galileo and Kepler's works would have been banned in 1616 and the Dialogue would have never been commissioned or published in 1632.
Cdl Hohenzollern was also given an assurance in 1624 that heliocentrism would never be condemned as a heresy by the Pope.
Galileo's charge "vehement suspicion of heresy" was just one particular charge that the Roman Inquisition issued. Obviously Galileo had argued for something that their consultants thought was a Heresy. But even worse - he had disobeyed a court order of the high ecclesiastical court.
The Inquisition sent out notes to the Papal Nuncios after 1633 to make it clear that Galileo wasn't a heretic. Mostly in order to make it clear that he had broken and abjured. A kind of gloating.
@jben1968@HistoryLA Nadie fue quemado por defender el heliocentrismo o por sus ideas científicas. Galileo fue condenado por desobedecer una orden de 1616 después de intentar defender lo que era hasta entonces una hipótesis usando la interpretación bíblica, algo condenado en Trento