You copied and pasted text from Illustrator into Photoshop.
The text came in looking just like it did in Illustrator.
I don't understand the rest, but I'm thinking you are asking if you can copy the style like in Illustrator and InDesign? The answer is no. You can save a character style from Illustrator or Photoshop in to your CC libraries and then use that to format more text.
1. After you pasted the text, go to the font styles panel in photoshop
2. If the format was copied from the Illustrator, you see the small plus icon after the name of the font style
3. To get rid of the copied format from Illustrator just go to the small menu on the right corner of the font styles panel and click the "override" function. So the default style of the document will be applied and the copied illustration format will be reset.
I post a picture how it looks like on my computer. (my CC is in German)
Hope it helps,