I use "tote" referring to a specific kind of bag, "a tote bag", usually made out of canvas material. I use it less frequently as a verb, but it's possible. I might use it to indicate what I am carrying is fairly small. "I've been toting this camera around all day." More likely, I would say "carry", but "tote" is ok too. I'm a Native U.S. English speaker.

Tote is quite an uncommon word, but the two words have essentially the same meaning. So I don't think there is any situation where it is necessary to use 'tote' compared to 'carry' or some other word.

Tote is very old-school and rustic. Don't use it.

I've noticed 'totes' being used in slang recently in social media to mean 'totally.' I think its a bit odd that way. Example: That is totes adorable.

I don't think I've ever used the word 'tote' in my life.