I've been in the process of developing a site in SharePoint 2010, which is composed of a set of different Farm deployed Web Parts. I was wondering what the process was for porting them to SharePoint 2013? I've been told that the Office365 and Farm-based versions of SharePoint 2013 are essentially equivalent now so is it possible for me to import them? Or will I need to convert them to Sandboxed solutions somehow?
Office 365 only supports Sandboxed Solutions and SharePoint 2013 Apps in the next public release.
In order to get your webparts running on Office365 you've to provide them as a Sandboxed Solution.
If you would see your webparts as part of the new SharePoint Store you have to create them as SharePoint Apps. Only Apps can be deployed to the SharePoint 2013 Store.