Copy, not export, a table from Arcmap

Your screen capture shows nicely how to copy current cell value to the clipboard. To copy selected records, right-click on the left-most gray button (where the 'triangle' is shown in your screen capture) and choose Copy Selected. Note: keyboard shortcut for both is Ctrl + Shift + C.

This is one of those annoyingly simple but obscure software things. If you just right click on the grey boxes over on the left of the attribute table and select "copy selected" there, you will get the whole tuple, not just the field your mouse happens to be over. You'll be able to paste the table as tab separated plain text into whatever application you please.

r-click on grey row heading bars, at left

This seemingly simple task has been toying with me for years...

I knew to select all, click left grey column,click copy selected to copy all and then paste fields into excel.

What I didn't realize until troubleshooting today (Arc 10.3.1) is that keeping the attribute table open is the only way it works on my system. If I enlarge to full screen and then "X" it out before looking to excel or another program it will not work.

I hope that helps!