Joe Biden should step down/step aside ...

[optimistic pessimist]

Joe Biden should step down/aside from the presidential race.

Regarding the choice between the two words, is it correct to say "step aside" is closer in nuance to "pass the torch"?

 

[5jj]

I don't think so.

 

[Margaret Cavendish]

Joe Biden should step down/aside from the presidential race.

Regarding the choice between the two words, is it correct to say "step aside" is closer in nuance to "pass the torch"?

Step aside carries a similar nuance as stepping down, but it is improper in this particular context. Joe Biden is stepping down from the Presidency. He is not stepping aside from the Presidency, although he IS stepping aside to allow Kamala to run.

The nuance that is similar here is the act of resigning, but 'step down' does not connote the same sense of 'allowing someone or something else to proceed' like 'step aside' does.

FYI I am not a teacher, but I am a native English speaker.

 

[probus]

With respect, @Margaret Cavendish, I disagree. Joe Biden is currently the president. "Step down" would imply that he is resigning the preeidency. But he is not. By declining to run for re-election he is merely stepping aside so that others may run as the Democrat party's candidate.

 

[Margaret Cavendish]

With respect, @Margaret Cavendish, I disagree. Joe Biden is currently the president. "Step down" would imply that he is resigning the preeidency. But he is not. By declining to run for re-election he is merely stepping aside so that others may run as the Democrat party's candidate.

You are correct about current events. I disagree that step down is incorect though. I'd argue that dropping his campaign is equivalent to stepping down from the job. I think the nature of this position obfuscates things a bit. Is quitting the race not effectively the same as quitting his job with a 5+ month notice? I have also seen this phrase used this way in the news today so I know that it is being used like this.

Though the way you word it is certainly dominating headlines

He didn't simply decline to run. He quit his campaign. He stepped down as a potential presidential candidate. He put in his notice.

 

[emsr2d2]

Perhaps it's an AmE v BrE difference but I would take "stepping down" to mean "resigning with immediate effect" or, at least in a normal job, "resigning with the minimum legally required notice period". I had a little dig around on Google and found that the 25th amendment of the US Constitution says that if the current president dies or resigns, the Vice President automatically takes over the position (there is no mention of a specific notice period). To me, that means that if Biden had "stepped down" on July 21st, the US would now be governed by President Kamala Harris.
He has stepped aside in the race to allow Kamala Harris to take his place in the race.

 

[Margaret Cavendish]

Perhaps it's an AmE v BrE difference but I would take "stepping down" to mean "resigning with immediate effect" or, at least in a normal job, "resigning with the minimum legally required notice period". I had a little dig around on Google and found that the 25th amendment of the US Constitution says that if the current president dies or resigns, the Vice President automatically takes over the position (there is no mention of a specific notice period). To me, that means that if Biden had "stepped down" on July 21st, the US would now be governed by President Kamala Harris.
He has stepped aside in the race to allow Kamala Harris to take his place in the race.

Personally I try to consider linguistics from a more descriptivist view. Anybody who says that Joe Biden is 'stepping down' probably has read the same headlines you have, and understands the same facts, but is expressing that same idea with different words because they are conceptualizing these ideas differently. That's why I said that I think the nature of the Presidency kind of obfuscates things here. To me 'stepping down' only connotes the idea of resigning immediately but I don't consider it an implicit part of the definition. To me it is closer to 'withdraw' although I definitely pick up on that same connotation as well.

Personally, I share your conception of the phrase, but I have seen it used in this way as well. I only phrased it as I did because it was what OP asked about.