I'm pretty sure that vertical bar and colour is how ‘wild’ they are at the start and thus how difficult they would be. I usually try petting them once and then rotate treats, petting, and prayers. I haven't found the lasso to be much use personally, but I've seen it reduce that vertical bar. 

Crafting treats often does the trick for me when I really want a horse. There is a certain [SPOILERS]-tagged wild horse preferred treat horse in Game Discussions that I like to reference in another tab when I get the breed. For example, if I see a wild Irish Cob or Clydesdale, I will make a combined treat using their preferred base ingredient, then make a sweet version of it with molasses. I try to get to the 75% call the horse mark on these guys unless I feel like they're ready to run, in which case I'll use a whistle. Fortunately, I've noticed that if they run during a treat offer I keep the treat. 

Horses I care less about I usually try whistles on when they're 30-60%ish. If they keep dropping when I pet them I use the whistle sooner because I don't have unlimited treats. Those horses get away most of the time, to be honest. 

So higher the bar, the more wilder the horse is?

I believe so. Same with the background colour for the wild horse icon. I think I saw red, yellow, green, and blue, with red being the wildest. It aligns with that vertical bar. 

That being said, it's an RNG game, too. I've definitely caught red horses after just one pet and lost horses I got down to green and blue.