In a certain sense, public speaking is no different than those situation. Even better, the people you're in front of you don't really care about, where as you do care about your family and friends. In other words, it should be that embarrassing yourself in front of friends and family "should" be the worse thing since you will have to face them again where as you won't have to face these strangers you're speaking in front of.
And yet, even though I've given ~10 public talks I still feel those butterflies, at least until the talk actually starts. Once it starts, for me, they go away. That assumes I know my topic. I'd say a best person talk at a wedding is more nerve wracking, for me, than a talk about anything I'm working on. I can talk about what I'm working on easily because I know it inside and out. Sure I need to practice my talk but if someone came up to me in a hall and asked me about my work I could talk their ear off with no practice. Conversely, the wedding talk topic is not a topic I know inside and out, hence it's harder, at least for me.
I know it was certainly nerve racking the first time I had to give a public talk at school. I wonder if the teacher had asked in private, something like
Teacher: Are you nervous about your talk?
Student: Super nervous
Teacher: Do you have a favorite video game?
Student: Yea, Minecraft
Teacher: What do you love about it.
Student: (with teach prompting, goes on for 5-10 minutes what things they love about Minecraft, things they made, experiences they had...)
Teacher: You just gave a public talk to an audience of 1. Just organize and practice a little and you'll do great!
I don't know if that would help but I'd like to think it would.