First I warped a text as a wave in Photoshop. Wrote the same text (the same font, size and other properties) in Illustrator and it warped differently - the warping is almost unnoticeabe although the bending is the same (50%) in Photoshop and in Illustrator. Why this happens and is there a way for this text to be done the same in Illustrator? Thank you!
Photoshop seemingly tries to retain glyphs of the text object somehow in proportions when a preset warp is applied. Try the same warp to a rasterized text and you will get the same as in Illustrator.
In Illustrator the only way to get the same for a text object as in Photoshop is to apply Envelope distort > Make with Mesh. Select 1 row x 3 column mesh and edit the nodes manually with the direct selection tool. It's difficult to get exactly the same result.