That's an intriguing question! I find that I shoot in different ways, which often depend on what equipment I'm using.
If I'm using medium format or large format gear I'm MUCH more deliberate in shooting. Although I rarely use LF these days due to cost, my Hasselblad, Rollei, and Super Ikonta are among my favorite outfits. If I'm going out on a specifically photographic journey, my eye is constantly looking for objects or settings that please me in some way, by virtue of textures, angles, juxtapositions, etc. If I'm in an urban setting, I'll generally find some design element that is pleasing and wait for an interesting looking person to enter the scene and position themselves. For instance, a few weeks ago (pre COVID-19) I was going for a mid-day walk when I saw a long, curved metal bench made of slats. The shadow of the 23 story building across the street was falling in such a way that it bisected the S-curve of the bench at a pleasing angle, and a strong cloud pattern was showing in the reflective surface of the skyscraper. So I set myself up with a 50mm on my Hasselblad. And waited. And waited. I stood there for more than a half hour waiting for someone to sit down on that bench. I finally shot it as a still life, but it would have been so much better if someone interesting had come along and sat down on the S-curve. If I'd been shooting 35mm, I would have probably tried more variations on that still life theme, switching lenses, positions, and angles. I wasn't able to return to that spot before the lockdown, but I'll go back and try it again sometime.
Whether I'm in the city or on a hike, I generally look for interesting textures, shapes, and juxtapositions, whether manmade or natural, before composing an image in the viewfinder. I often use a spot meter to visualize the final effect of the brightness range on the scene, and place the values accordingly, taking a few minutes to work out the angles, camera position, and lens (if I'm using a camera with multiple lenses, of course...). If I can't find something that pleases me in the viewfinder, I often move on without pressing the shutter on medium format expeditions. If I'm shooting 35mm or digital, I'm much more inclined to take a couple of imperfect shots and hope to get the image I visualized through post processing through crops, tonal adjustments, etc.
That deliberateness is exactly what brought me back to film from being all digital for several years. I like working slowly and exploring possibilities when I see something that interests me, and it's all part of the artistic process. In this way, it's kind of like fly fishing; I can have a lovely day of fishing and never get a nibble or an enjoyable walk through the city or woods without ever pressing the shutter.
Thanks for making me think about it!
Andy