I'm not a revolutionary and I disagree that the semantic difference is unimportant.

"The system must be destroyed" implies, assuming we're talking about national politics, at the very least a short period of very deep constitutional and institutional reform, but really refers to nothing less than civil war, violent revolution, and the systematic dismantlement of existing institutions from which proponents of such action generally assume that their preferred method of government will naturally emerge.

This is opposed to a belief that, flawed may they be, democratic institutions also act as safeguards against the tyranny of the majority as well as the tyranny of whoever has the most money/guns, and slow incremental change to these institutions is preferable to their dismantlement.

Of course everything in the world isn't so black and white. Nonetheless the existence of gray doesn't diminish the difference between black and white. "The system must be destroyed", by virtue of the violence it implies, is an extremist statement and different in nature to "the system must be fixed".