Is transparency portable to apps outside of PSE?

I expect positive answers to this one, mainly because I've been able to save items from Hemera's The Big Box of Art, in which the artwork was embedded in the familiar grey-and-white-checkered pattern which was effectively transparent when I set it as a layer on top of a background.

There's something I don't know about PSE -- there's A LOT of things I don't know about PSE -- because I created an image embedded in transparency and saved it as a .jpg file.  I intended to position that over a background in a different app where I was building a collage and I hoped the transparency would do its thing.  It didn't, because in its exodus from PSE, the transparency part survived as solid white.   Please tell me how to do this the right way.

Once you've done that, I have a couple of questions related to this.

(1) Based on what I said above, this feature is obviously not unique to PSE.  Is it considered to be an "industry standard"?

(2) If the answer to the above is Yes, can I expect to see it used in most, if not all, of the apps that deal with artwork this way?

Thanks for any help.