Legally, there are not two categories of conspiracies; there is only one, and it as follows:

"An agreement between two or more persons to jointly commit either an unlawful act or an act which is lawful by unlawful means."

https://encyclopedia.lexroll.com/encyclopedia/conspiracy/

Note that this definition requires an agreement, not merely a pursuit of the same goals or targets.

The second "type" of conspiracy you describe above lacks the meeting of the minds required to establish an agreement. What you have, in fact, described is actually groupthink (which I actually think occurs far more often than conspiracies, especially in the current climate).

Bottom line, it's become increasingly clear IMO that conspiracies are conveniently found when they support a political agenda and conveniently disregarded when they do not.

Indeed, nothing new under the sun in that respect.