Which event are we talking about?

The ones that agree with my sensibilities are protests. The others are riots.

Are you being facetious, or are you really saying the definition of a riot or insurrection change according to your preferences?

I think they are comparing Jan 6 with the summer's BLM protests.

I don't have a fully coherent argument why the two are different, but intuitively I think they are very different. For example, one was a response to unchecked executive power (killings by police), while the other was incited by unchecked executive power (the president).

From my European point of view. One was response to conspiracy theory that cops are assholes biased black people (much more likely that cops are assholes in general), second was response to conspiracy theory that democrats stole the election (much more likely republicans just didn't vote by mail). That said, attacking government building during recent riots makes much more sense then previous BLMers looting and setting on fire random supermarkets/buildings which were not related to cops or government in general.

Or even the HK protests. I could list many famous [protests|riots] in history and they would also make great examples.

I am not referring to any real life events.