When you click the 'Edit Image' icon on an image that has been inserted into a page/post, a dialog is displayed that allows you to edit various properties. One of these fields, the Alt Attribute, has a label called 'Alternate Text'.
When you click the 'Edit' link next to an image in the Media Library, you can also change the properties of an image (or file). Again, one of these fields is for the Alt Attribute. This time however the field has a label called 'Alternative Text'.
These two fields should have the same label, for consistency. (As a sidenote, previous versions of WP have used 'Alternate Text' rather than 'Alternative Text')
This was using the latest nightly build.