If I am in the woods I wear hiking boots - if I am on pavement I wear sneakers.

If you are walking on a sidewalk or other relatively smooth surface, walking shoes are best.

Hiking books have important purposes. The ground on a trail is rough and uneven. The firmer sole of a hiking boot protects the bottoms of your feet from rocks which stick up and would be uncomfortable or even painful if wearing a softer bottomed shoe like a walking shoe. They also help stabilize your ankles from a twist. If you are wearing a properly fitting hiking boot, your toes will not bump the front of the boot when you go downhill on a trail. I know all this because I hiked for a day in walking shoes. My feet were very sore.

Hiking boots are also good in the woods for protecting your ankles from critters that might get your ankles...things that like to pop up and bite your ankle like rattle snakes...

I wear athletic sandals (Keen) for walking on pavement and on the treadmill because they give my high arches the best support compared to sneakers which I am not a fan of and rarely wear. Plus, they are SOOOO cushy which my feet appreciate. I wear them with low profile athletic socks b/c otherwise my feet sweat in them without socks. When hiking, I need ankle support since I'm prone twisting ankles, so my higher ankle Keen hiking boots come in handy even in summer...with the right socks. They also have good arch support.

Here is a link that might be useful: Keen sandal

This will be a word thing - when you say tennis shoes do you mean those white, no-support things or do you mean well-supported running, walking shoes (or maybe in your neck of the woods you might call them sneakers).

How long are your walks going to be and are they sidewalk walking, flat trail walking or hilly hiking.

For flat trail walking or sidewalk city walking I would use running shoes that have proper arch and heel support. For the next level I do wear a trail running shoe (I run in the trails and trail runners are built for this with a firmer sole, bigger tread and strong heel support. I've learned that because of the stiff sole they are uncomfortable to wear as a walking shoe for long walks)

Hiking boots are probably too much shoe for normal city/trail walking.

Tennis shoes for me are well built Nike's and the like with support. The walks are for now 30 minutes to an hour on sidewalk and through small parks.
Once I build up some more strength I will be walking through larger state-forest type parks.
I wore my tennis shoes for a walk with 2 dogs a while ago, no problem. Will walk 2 more dogs later.

My feet swell when I'm warm so I HAVE to wear sandals when I walk; I wear them from spring to fall, all day. Of course, they're supportive--right now I'm wearing mostly eccos.