It is sense #2 that drives philosophers much of the time. (not all of the time)
Then, the first distinction is between VALID arguments and SOUND arguments.
Try this: a sound argument is a valid argument with true premises.
Example: imagine a conversation 100 years ago between father and daughter:
D: Soon I will be 21 and able to vote!
F: Well no, you won’t.
F: Only persons 21 and over can vote. And, females are not persons; so, you cannot vote.
D: I see that’s a valid argument, but the premises suck!
How should the daughter proceed to convince her father?
“Yesterday was a great day for the women of Saskatchewan,” the Feb. 15, 1916, issue of the Regina Morning Leader proclaimed.
At the time, the Dominion Elections Act, which dictated how provincial elections were run, stipulated “No woman, idiot, lunatic or criminal shall vote.” On Valentine’s Day 100 years ago, the government decided it was time that change.
Good discussion here.