I've ran into a few clients before in public. You both kind of make eye contact but then look away. I've never had someone make it so obvious or creepy like. The only time I was a little uneasy is when I was picking up a prescription, but even then I didn't make it seem like I didn't want to say who I was or what I needed. I think when you draw more attention as to not wanting to be seen, is when people, if they are with you or him, seem to want to ask questions like who is that.
And like how you said, depending on the friendship and if you or they are with someone, I may or may not just politely say hello or how are you.
oh it happens alot..in fact one of the reasons I dont show my face in pics anymore is because I was recognized at an establishment I was at one night..the gent emailed me the next day and told me the spacific drink we had together!! This town isnt really all that big....he and I still joke about it!!