"Presence" and "projection" are often overlooked as concepts at the expense of "loud". There can be a difference. And even then, it can be deceptive. I used to play in a professional band who's lead player had played lead with Woody, Stan and Toshiko just to name a few. Once, he was yelling at me, "play louder" several times in a row and I was on the verge of a double hernia and yelled back at him, "I'm blowing as loud as I can! And I can hardly hear you!" And he later told me that "loud" also meant a concept of sound. His was to project a corkscrew of sound forward. When I heard a playback of our playing, he was definitely right at the fore, no question who was leading the band.