When Rein used the Divinity Slash, for a moment he felt like he was able to execute the Sword God Art move but the very next moment he realised that he was still lacking a little bit and what he executed was not the true Sword God Art, at best it was a close imitation of the Sword God Art.
It looked very cool from the sides though and both Tasha and Stella were fascinated by it. Only Anna noticed that Rein was actually unable to unleash the real God Art but she was still happy as it was considerable progress for Rein.
But what Kenshin executed was a real Sword God Art move. For a second Rein felt like the whole world was pressing down against him. He almost had an illusion that the sky was breaking apart and the world was coming to an end. In this situation, suddenly his survival instincts kicked in and his move changed slightly.