This tree is right next to a paper mulberry in a backyard (not mine). It grows little red fruits which the starling birds will eat from when ripe. I've also seen it blow what looks like puffs of smoke (I couldn't post a video of it). This tree grew very fast, to about 30 feet within the past few years. Is this also a mulberry?

It does look like a Mulberry to me. A picture of the fruit would help pin it down.

I can't get very close but the fruit is in the middle picture, the little red ball dead center.

Porkpal is right about the mulberry.
Brenda-- Paper Mulberry's are separate male and female trees. The female trees do have an edible red fruit. The male's do not. In my vicinity they are all males, I have never actually seen the fruit but your picture looks like other pictures of the fruit. But everything else leaves and bark that was with your other question would be true whether male or female. In my area they are very invasive without the female. I can not imagine how much more invasive they would be with the female tree. Many blessings for a joy filled week!

Brenda--After reading some old botany journal entries on the web. It does state the male tree will throw it's pollen all at once. It will look like puffs of smoke. I wonder if that is a phenomenon that happens when the female tree is close. I have never seen any of the male paper mulberry's pollen explode, and I work around them all the time. Next year I will be on the hunt fot exploding pollen! Cool! May you be surrounded by peace!

Funny, it's seems to be the female tree (the one with the fruits) that are the pollen blowers. I can send you a video of it, although the tree hardly had any leaves on it. The male tree (the one with that unique leaf shape) is not nearly as tall and it seems to be the only one so far in my neighbors yard. I did happen to go to a local city park in Brooklyn an noticed the male paper mulberrys lined along the outside edges and it appears they're already starting to choke the life out of some adjacent trees (whose idea was it to put such an invasive tree in a city park?)