An interactive form (AcroForm) is a document where the fields are real objects: each has a name, a type (text, checkbox, dropdown), and a position on the page. Such fields highlight when opened in any decent viewer, you can move between them with Tab, and the entered values are stored as data, separate from the form's artwork. These are filled directly – you type values into the detected fields.
A flat form is just printed layout: rules, boxes, and captions are drawn, but the document contains no fields at all. Scanned paper forms and exports from legacy systems usually look like this. You cannot type 'into a field' because no field exists. Here an editor does the job: text is placed on top of the page at the right coordinates.
Two closing notes. Before sending, a completed interactive form is often flattened – the values become ordinary page content, so the recipient cannot alter them by accident or on purpose. And if the form calls for a signature, that is a separate step after filling, not a replacement for it.