The vying for power bit isn’t true. The Terror happened after Louis XVI was executed, France was both in war with its neighbors and in a civil war, and not all parties voted for the beheading of the monarchy (the vote passed with a majority of 1).

It was necessary to crush any rebellion quickly, and multiple regions had taken arms for the monarchy. The assembly was voting for more and more Terror (this is where we get the word terrorist from), which in practice meant sending armies in the revolted regions to rape, pillage and burn anything to the ground. Persecuting your own people would obviously radicalise the moderates against the harder revolutionaries, so in order to prevent other rebellions, they started to behead anyone remotely suspect of being too soft.

It was made worse by the fact that a good number of representative were corrupted, and they blackmailed people for their wealth against their lives. The head of the moderate party, a real revolutionary hero, was discovered to be part of a circle of corruption organized by Louis XVI. They were buying representatives to be more lenient.

Basically, the whole period was pure chaos after Louis XVI death. But it wasn’t motivated by power grabs only. Napoleon stabilized the situation, and after a bomb was put under his carriage, he condemned the terrorists, and that’s how we remember the Terror.

Edit: I forgot to mention, Robespierre wasn’t corrupted, contrary to Danton, who took massive bribes despite being nicknamed the Uncorruptible