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I'm confused which one should I use to mark an item as favorite.

15

The like will show up as part of a count, and people you are sharing with will see when you like something. Your stars are private and only you can see what you have or haven't starred.

If you want to track something to look back at later, use a star.

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6

This post explains the differences.

The ability to "Add Star" is Google Reader’s equivalent of a "read it later" tool.

When you click on the "Like" link at the bottom of a feed item, your name is simply added to a list of all other people who also clicked "Like" for that item.

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