I agree with Basil that, in most everyday situations, you would avoid going into the precise details. Among friends, family, colleagues and so on, I'd say something vague like 'upset stomach'. For example:
'Would you like some orange juice?'
'Umm, no thanks. I've actually got a little bit of an upset stomach, so I'll just have some water.'
Your friends and family would not want to know any more details than that!
You would only use 'loose motion' or 'loose stools' in a medical context. Doctors and nurses use these terms - they would not be appropriate other contexts. It isn't that these terms are not polite, it's more that they are rather too detailed and unpleasant-sounding.