can the same model be used with different set of data?

If your product itself is an independent variable then yes. As long as the attributes used to make your prediction are common there is no reason why models cannot be reused.

Typical example would be a sentiment analysis model, when properly trained you should be able to use the same model to predict movie sentiment or product sentiment, but naturally models will perform better if the domain is the same.

So maybe the actual answer is : it depends ...

Also whether you can mechanically reuse a model to generate predictions is separate from whether the model is going to make sensible predictions for the new use case.  In the case of demand forecasting, you would need to ask yourself whether the relationships captured for the product on which the model was originally built are likely to be consistent with the relationships you would expect for the new product.  If they are similar products then this may be plausible.  But if the products are different, then this is likely not a good assumption and you would be better off training a new model on the other product.