I think "spine" has a connotation of morality, whereas "balls" is about pure daring.

But yeah more or less synonymous and you're right that it's definitely used as a euphemism for the stronger version. But also slightly different connotations depending on context, imho

All things being equal, "grow some balls" is a gendered statement. It implies you need "balls" to be strong or able to form coherent arguments or defend yourself.

I can see why someone would intentionally use an alternate phrase.