I agree completely. It's all in how sensitive the sensors in the device are, as well as where on your body you have the phone most of the time.
I know on my Note 4, it will often show some running that I know I never did. I'm 6'2" though, with long legs and I tend to walk pretty fast, especially at work where I get the majority of my steps for each weekday.
I'm sure walking vs. running has something to do with amount of time between steps that the sensor detects. There must be a cutoff between what it's programmed to think is walking and running, but I'm not sure what that is.
As far as up and down, I'd say it's more of the same, but also depends on where you have the phone. If it's in your pocket, it's going to be laying mostly face up or face down, or turned on its side (basically landscape mode), while when you stand up, chances are it's in more of a portrait mode orientation. Not sure how that translates if you've got it in a holster on your hip and it doesn't really change orientation between sitting and standing though.