1. 제발 is much stronger than 좀.
The speaker is likely to be either very annoyed or desperate to say this.
Please spare my life.
Please stop doint that.
2. 좀 is a milder expression.
좀 살려주세요. ( This doesn't make sense if you are really begging for your life. It only does when you use "spare my life" figuratively and mean "please help me or my dad kill me.", etc )
좀 그만해. (a milder version of 제발 그만해)
3. You can also combine the two and say "제발 좀" to make sound even stronger than "제발".