Copying a metric makes a separate version of a metric. It duplicates all of the data and chart settings as the original, but it is an independent metric. So if any changes are made to the original, it doesn't affect the new copy (and vice versa).
NOTE: Copying a metric will add a new metric that counts against your metric limit, even if you don't make any changes to it. If you want to copy an identical metric to another dashboard, you can use the "Share" option.
"Copy Metric" lets you create a copy of a metric and immediately save it to any dashboard.
Copy and Edit
"Copy and Edit" will open your copy in the metric builder, where you can make any changes to the metric. When you save the metric, you will then be prompted to select the dashboard to save it on.