The Galaxy S9 and S9+ haven't changed much from the Galaxy S8 and S8+ that preceded them, with an extremely similar design and materials. That'd lead you to a totally realistic expectation: that a Galaxy S8 case would fit on the Galaxy S9, and a Galaxy S8+ case would fit a Galaxy S9+. Right? Wrong.
The Galaxy S8 measures in at 148.9 x 68.1 x 8mm. Compare that to the Galaxy S9 at 147.7 x 68.7 x 8.5mm. 1.2mm shorter, 0.6mm wider and 0.5mm thicker. The Galaxy S8+ is 159.5 x 73.4 x 8.1mm, and Galaxy S9+ is 158.1 x 73.8 x 8.5mm. 1.4 mm shorter, 0.4mm wider and 0.4mm thicker.
A Galaxy S8 case could tide you over for a few days, but you should buy a new Galaxy S9 case.
At first glance the size differences are so close that the Galaxy S9 or S9+ will actually "fit" in the old case, and the ports and buttons are all close enough to work with cutouts. But then you'd flip the phones over and notice that on the Galaxy S9+ the second camera was covered. On the Galaxy S9, the fingerprint sensor would be obscured.
If you have a Galaxy S8 or S8+ and make the upgrade to an S9 or S9+ you could use your case on the new phone for a few days while you wait for a new purpose-made case to arrive for the new phone. But don't do it for longer than that. An ill-fitting case is just about as bad as not having one at all — it's not going to provide the protection you need.