Everyone's feet and fitness level is different. Shoes / boots that are ideal for one person may not work for another. As a tall (183 cm) heavy (114 kg) fellow, I must have the addition support that mid-high Keen hiking boots provide. Also, my rucksack weight is regularly too heavy (my bad) and I know it. But I digress...
Someone who is shorter and lighter, and perhaps carrying less of a load will do as well with lower trail hiking or running shoes. But, before you make the investment either way, try to assess whether you can walk all day, in all weather conditions with a loaded rucksack in the footwear you choose. Practice in the sports shop with various shoes. Bring your loaded rucksack. I use a 7 kg sack of kitty litter in my rucksack for practice. Once I add a couple liters of water, I am up to the target 10 -12 kg I customarily carry...at least at first... But, again, I digress...
The height of the shoe, and the stiffness of the sole a influence mostly by your size, total (all-in) walking weight and physical capabilities. Between trail runners and low hiking shoes, please know that trail runners are intended for folks running trails over varied ground with either no rucksack or just a small day bag. Hiking shoes have additional cushioning, thickness and stiffness in the middle layers of the sole and upper to provide improved stability and comfort.
Beyond this, remember the sizing mantra. Start with your street shoe size. Add 1/2 size for two pair of socks, another 1/2 size for foot swelling after several hours walking under load, and a final 1/2 size to account EITHER for splaying of feet (widening) after several weeks of sustained walking under load, AND to provide enough room in the tow box so your toes NEVER bump against or rub the inside of the toe box on a downhill stretch.
That is why my US size 11 (45 cm) street feet, wear a size 13 (47) Keen Targhee on Camino. This is listed as two full sizes larger than my street size. However, Keen lists these boots on their web site as running 1/2 size small. So, the size 13 (47) is actually a size 12.5 (46). In the end, they fit comfortably and work outstanding FOR ME. I have worn the same pair of Keen boots for three Caminos.
After each pilgrimage, I send them into a firm that specializes in factory specification resoling of most all brands of hiking and running shoes that have vulcanized (melted and glued on) outsoles. I do this because resoling costs 2/3 the price of new boots, and this pair is so well broken in that they fit like gloves. I have another brand new pair of the same boots in the cabinet, provided free by Keen in a warranty claim after my first Camino. However, they do not get used until the upper boots become unserviceable.
All this said, some people have feet that do not swell after a day's walk with a rucksack, or splay after several weeks on the trail. I understand and respect that, as everyone's feet are different. However, at the risk of incurring the wrath of DougFitz, I will be categorical for a moment...NEVER, EVER buy shoes in your street size to walk the Camino. You WILL be sorry.
The cause of many blisters and too many lost toenails is wearing shoes / boots that are too small for the purpose. Also, you must learn how to lace your shoes / boots so that the foot is well supported and the heel is retained in the heel counter. If your foot can slide forward, your toes will strike the inside of the toe box repeatedly. This causes irritation, blisters, bleeding and lost toenails. Have a look at this web resource for lacing suggestions:
http://www.fieggen.com/shoelace/
Also, search You Tube for "how to lace hiking boots." There are tons of videos. There are too many variations to describe. Some are for style and fashion. Other methods are functional. On the Camino, always opt for function and utility over style. You will not be sorry.
I hope this helps.