Tu me manques...
So, I miss you in French is Tu me manques
which does confuse me a little bit seeing at for example to say I love you is je t'aime.
But what confuses me is that apparently, to say 'I don't miss you' is
'Tu me manques' - I miss you 'je ne te manque pas.'- I don't miss you
'Je te manque'- You miss me 'tu ne me manques pas'- You don't miss me
Is that right?? And if so, why the difference between the positive and negative statements?
There is no difference between the positive and the negative statements, as mentioned by others. Your translations of the negative versions are incorrect.
In some cases, the two verbs work the same way in English and in French:
- I missed the target = J'ai manqué la cible
- I missed you by a whisker = Je t'ai manqué(e) d'un cheveu
But, when 'miss' means 'long for', they work the opposite way:
- I miss you = Tu me manques
- I do not miss you = Tu ne me manques pas
Well, I think I can explain why. It is because we only have here the version with 'me', so it looks like 'tu me manques' literally means 'you miss me', which is not the case at all. I will change the subject of the English sentence, to clarify.
- Your brothers miss you = Tu manques à tes frères.
You can see there is the added 'à', which is not visible but only implied when we use 'me, te, se, nous, vous, leur'.
- Tu me manques = Tu manques à moi
'Tu manques à moi' is grammatically incorrect, but we could say: 'Tu manques à qui ? À moi.'
So when 'miss' means 'long for', in French we use 'manquer à' (transitive indirect), and not 'manquer' (transitive direct).
But we must be careful, because 'tu me manques' could also be transitive direct, if it does not mean 'long for'.
- Chaque jour, tu me manques (transitive indirect) = Every day, I miss you (you are missing to me)
- Chaque jour, tu me manques [d'un cheveu] (transitive direct) = Every day, you miss me [by a whisker]
Manquer is a strange verb in that it is used differently than others. As noted, it is not used as he/she misses someone, as aimer is for loving someone. It is more like he/she is missed "by" someone. Another verb with somewhat of a similar construction is se interesser. It took me a while to get both figured out.