If you would add a title field to the notes, as well as a type (invoice or quote or all), it should then be (relatively) simple for a user to select a note during adding invoice / quote.

If a note is marked as default, then that would be the pre-selected note.

However, a dropdown list would exist for choosing from all the possible notes. That is, during add invoice, the dropdown would include notes tagged as being a type for invoices or for all.

And of course same would exist for quotations.

Another option might be to have a fixed default note, one that is always included, but then allow for a secondary note to be selected and appended to the default. This approach would allow the creation of a standard note on all invoices ("Thank you for your business" etc) and also provide some quick extensions w/o typing or cut/paste ("Widgets are covered by a factory warranty..." or "Repairs are guaranteed for 30 days..." etc)