Hi, Marlena. Illuminated Cloud doesn't have the exact same mechanism as the Team Synchronize view in Eclipse, but it does have a feature that is close. Basically when you retrieve metadata using Illuminated Cloud, the retrieved metadata is placed in a temporary directory and is displayed in a directory comparison tool with the retrieved metadata on the left and the local project metadata on the right.
By default IntelliJ IDEA's built-in directory comparison tool is used, but you can also configure it to use your own favorite external diff tool such as Beyond Compare, Araxis Merge, WinMerge, DiffMerge, etc. I personally use Beyond Compare. These external tools can generally be configured to show both directory and file differences in a much more usable manner. For example, you can have it show only files that differ and/or are newer on the left, and you can have it ignore "unimportant" differences such as whitespace-only changes. Here's an example of Beyond Compare showing the retrieve results with two changed files and four new files:

The big difference between Eclipse's Team Synchronize view and Illuminated Cloud's comparison is that the latter isn't bidirectional. You can copy changes from the retrieved metadata into your local project source by copying left-to-right, but copying right-to-left will have no effect. Instead after you retrieve and merge the retrieved metadata into your local project source, you can perform a deployment to send updated local metadata to the org. You achieve the same goal, but it's two explicit steps. For example, in the screenshot above, if I wanted to keep the local changes to ShoppingListMobileListControllerTest but bring in the new files and the changes to expenseTracker.app, I would use Beyond Compare to copy over everything but ShoppingListMobileListControllerTest.cls and would then perform an incremental deployment to catch up the org.
Hopefully this helps, but please let me know if not!
Best regards,
Scott Wells