what is the difference between the messages "Integration up and running" and "Integration Ready?

Hi,

Both are pretty similar.

When you see "Integration Ready!", that means you have successfully integrated your form with Google Spreadsheet. This is the last step of the Spreadsheet Integration Process. You can click on the generated spreadsheet link to view the populated submissions forwarded from your form every time you received submissions from your form users.

Example:

When you open again the Google Spreadsheet Integration from the list. You will see the following message, which means your form is already connected to Google Spreadsheet. That's what exactly "Up and Running" means.

You can disconnect the integration by clicking the "Remove Integration" button if you want or if you need to re-integrate your form to Google Spreadsheet.

Hope this information helps!