I am being offered a PhD studentship in the field I am interested but the precise topic of research is different from my interests. Should I take it? Will it make any difference, if, later I look for a post-doc (in the same field) but a different topic.

I'm afraid your description here is too vague to say yes or no. In many subjects people are able to change specialisation quite easily when they start a post-doc, however sometimes experience in a particular technique can be a requirement. Ask people who know your field whether you'll be able to move. You should remember that doing a PhD where you have no interest in the subject is not a very good idea - it's hard work that requires persistence.

The project in question is industry specific. I prefer to work on a project thats different but requires same techniques and theory (ie its aimed at another industrial product). If I refuse now, I might have to wait a year or two.