These are the same, right?

pretty much

reporting comments for behavior that you yourself have just engaged in

Upon receiving a disrespectful reply, some people will simply reply with an equally disrespectful comment, without reporting. When the initial disrespectful user then reports that reply, it's hypocritical. They will be reprimanded too, even though their original disrespectful comment was not reported.

So making only one report would be appropriate in that case?

People are making multiple reports of single users and maybe only one of the reports is valid. It seems people get angry with a user and just open that users account page and report all their recent comments. When you do this, your user name is attached to each report. This kind of report bombing will not be tolerated anymore.

It's ok to break the rules if you are in an argument?

The content policy of this website is well written, and calls for moderators not to be over-bearing, and for users and mods alike to be more tolerant than other similar sites have become. I think this is a great idea and it's my guiding mantra for moderation here.

This includes tolerating a little name calling here and there, which is natural during arguments sometimes, though it greatly weakens the name-caller's position. When 2 users are in a heated argument, calling each other names, and neither of them reports the other, my tendency will be to let them at it. If a third party reports one or the other or both, I might ignore that report since they are not involved. If one of the users in the argument reports the other, both will be reprimanded. if they both made disrespectful comments.