If you look in the Project Explorer in the VBA editor, there are actually two sheet names. The name on the left is how the sheet is seen within VBA, the name on the right is the name given on the tab strip at the bottom when the user is using Excel. (By default they're both "Sheet1", that can be confusing.)
I find it easiest to use the first name; it removes the need to say Worksheet("Whatever"). If the name hasn't been changed, just use that.
Sheet1.Range("A1").Value = Target.Value
edit: As a note, the only way to change the name on the left is to make sure the "Properties" window is visible, click on the sheet, and then rename. I find it to be best practice to rename all my sheets right away, to avoid Sheet1, Sheet2, Sheet3. wsTotals, wsCoverForm, and wsConfigForm can make code much more readable.
another edit: The reason the other method isn't working is because it would have to follow this structure:
ActiveWorkbook.Worksheets("Sheet1").Range("A1").Value = Target.Value
That's the only way I could get it to work, I've had both work for me testing it out just now. It's a little less cumbersome to use the first way.