Although it may not be apparent for all users, Zotero has four different types of attachments. These are described below.
For most users, stored files are the "normal attachments". Stored files are stored inside Zotero's own data directory and can be synced to Zotero server or a WebDAV server. All files created by translators are stored files and dragging and dropping a file on Zotero will create a stored file.
Linked files are created by "Link to file" menu entry in Zotero. Zotero does not store the files for these attachments, but simply stores the name and path of the file. Because neither the path nor the file is synced online, these are not supported by ZotPad.
Starting from version 1.2, ZotPad can attempt to download linked files if they are stored in Dropbox. Because Zotero synchronizes only the filenames but not the paths of linked files to the server, using this feature requires that the files are named in a way that ZotPad can derive the file path form the item data. This will be possible if all the files are stored in the same folder, or you have stored them in folders based on e.g. authors or years. It will not work if you have stored the files in folders organized by subjects etc. This might change in future versions if there is sufficient demand for this kind of feature.
Converting linked files to stored files is possible with the ZotFile plugin for Zotero. After installing ZotFile, you can convert linked files to stored files by right clicking on a linked file and then choosing "Manage Attachments" -> "Rename Attachments"
Stored URLs are weblinks, which have been downloaded and stored in the Zotero data directory. These are most commonly websites, but in some rare occasions can be also PDF or other files. Stored URLs can be synchronized to Zotero server or WebDAV server and are supported by ZotPad.
Linked URLs are just weblinks that are stored as such without downloading and storing the file the link points to. ZotPad supports linked URLs and opens these in Mobile Safari.