Sometimes ideas are small and specific, sometimes they are big (ex. add a button vs. create an app that does x). Currently an idea is assumed to only be for a feature.
It is now possible to promote Ideas to Initiatives.
You can read more about it here: http://blog.aha.io/promote-big-idea-to-roadmap/
At this time, we do not have plans to promote Ideas to product. However, it is possible to create a custom field on your Idea to link to a product.
We have this issue today a bit and expect to continue having this issue. For now, we copy/paste the details over and close the Idea, but this would be a great feature.
I came here to post a similar idea -- often ideas correspond to multiple feature requests, it would be great if we could link them to multiple features.