I am not a tester for the new navigation. I applied to be a tester about two weeks ago but I am not until now. I am curious about what the 4 buttons do. You can see them it the screenshot. What do the 4 buttons do?
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Well, first I'll talk about the two top buttons. When you hover over them, it tells you what they do. The top left button says "Expanded layout toggle". When it is selected, you will see an expanded version of each question, meaning the title, beginning of question, tags, minutes/hours ago asked, and user profile with picture and reputation and badges are shown. Also, the votes and views are in an up and down fashion.
The top right button says "Collapsed layout toggle" when it is hovered over. When it is selected, only the question title, tags, time ago asked, and user profile with rep. The votes and views are shown in a side by side fashion.
The bottom buttons are pretty self explanatory based on what they show when they are hovered over. They will only be showed if two or more tags are being looked at. The bottom left button, labelled "any" says "Show questions with any of the tags". This means that it will show questions that have at least one of the tags specified, in your situation your favorite tags. The button right button, labelled "all" says "Show questions with all the tags" (this should be "all of the tags") so when it is selected, it will show questions that have all of the tags being looked for.