PDF forms, and why some cannot be filled
Two different things are called a PDF form. One has real fields; the other is a picture of a form, and no amount of clicking will make it typeable.
Why can I type into one form and not another?
Because only one of them has fields. A fillable PDF contains form objects, each with a name, a type and somewhere to store what you type; a scanned form contains a picture of ruled boxes and nothing else, so there is nothing to click into.
Telling them apart takes a second: press Tab in a reader. If the cursor jumps from box to box, the fields are real. If nothing happens, you have an image, and the form has to be filled by drawing on top of it.
What kinds of fields are there?
Text boxes, checkboxes, radio groups, dropdowns and signature fields, and each stores its value differently. A checkbox holds a state rather than a tick, and a dropdown holds the chosen entry rather than the words you see, which is why two readers can render the same field slightly differently.
Fields also carry names, and the names matter more than they look. Two fields with the same name are treated as one, so filling either fills both. That is deliberate for a name repeated on every page, and an unpleasant surprise after a merge.
What does flattening do?
It draws the current values onto the page and removes the fields. What was a form becomes an ordinary document that looks identical and can no longer be edited, which is what you want for a copy you are sending or filing.
It is not reversible. Keep the fillable original if the form will be reused and flatten a copy. Flattening is also the correct way to stop a recipient changing what you entered, because a filled but unflattened form is a document with editable answers in it.
How do I fill a form that has no fields?
Place text on top of it. Typing into position and then flattening produces a document indistinguishable from a filled form for every practical purpose, including printing and signing.
If the same blank form comes back every month, run recognition over it once so the text is searchable and keep one filled copy to work from. Rebuilding the fields properly is a job for whoever issued the form.
Where to go from here
Fill a PDF form works with the fields a document already has, flattening fixes the answers into the page, and the editor is how a scanned form gets filled at all.
Why editing PDF text is limited explains what is happening when you type onto a page, and electronic and digital signatures covers the box at the bottom of most forms.