Leave me alone works fine for both situations.

1. I would use the first one if i didn't want company. 2. I would use the second. Having answered your questions, if I didn't want company, I'd probably say something like "I'd prefer to be alone right now." If I wanted someone to stop bothering me, I'd probably say "Leave me alone!" in a tone of voice that made it very clear.

Please see this: https://www.italki.com/question/312785 That distinction is extremely outdated. Here's a reference to it: "Traditionally, there has been a distinction: leave me alone means 'leave me by myself (in solitude)'; let me alone means 'stop bothering me.' But only extreme purists will fault someone who uses leave alone in the nonliteral sense. Today that phrase is far more common than let alone." (Bryan A. Garner, Garner's Modern English Usage. Oxford University Press) Most native speakers today have never even heard 'Let me alone', and very few of us would ever say it. You may come across it in texts written a long time ago, and you may hear it as a dialectal variant in some regions. However, it is not standard English. If a native speaker in, for example, a community in the southern states of the US, were to say 'Let me alone', we'd presume it was a local variant. However, if you, as a non-native were to say this, it would be seen as a mistake. You would probably lose marks in an assessment if you were to use this non-standard phrasing. You should use 'Leave me alone' for both cases.

I think you are safer saying, 'leave me alone' when you want someone to go away! The other expression (let me alone) is not one I recognise.

Joni Kirk, thanks for your advice.