I Notice That Many Adults Have a Gap Between Their Two Front Teeth. Is This Always a Form of Periodontal Gum Disease?

Not necessarily.  If the gums are healthy and teeth are not loose, then it's usually a genetic trait passed on by parent or grandparent.  It may also be due to extra gum tissue called frenum that's present in the gap that may need to be trimmed if the gap is to be closed.

No in many cases it is caused by muscle called the frenum which can be removed good luck.   Kevin coughlin dmd MBA  magd. CEO Baystate dental pc

Thanks for your question--to answer it further, having a gap between two front teeth is not necessarily a form of periodontal gum disease.  Assuming gums/tissues are health, it could be a result of genetics, or even a result of the jaw/tooth size respectively.  Of course, making sure that gums and teeth are in healthy condition is a primary focus, and regular checkups will help to ensure this. 

The gap can be caused by a number of things.

It could be genetic. Some people have very large jaw bones and small teeth so there is always extra space.

There could be a muscle that attaches to the upper lip pulling on the gum tissue in between the front teeth. 

Some patients like having a gap as they believe it "adds character."

If the gap is not caused by periodontal disease (bone loss) then it only needs to be treated for cosmetic purposes.

It could be periodontal, genetic, or due to a frenum which extends between the teeth on either side of the gap