Mostly an evening, or "dinner at a nice restaurant", look for me because I can place it on my lap under the napkin--which I was taught was the correct place way back in the times when evening bags and gloves were part of formal attire. I almost always toss a small clutch in my travel bag for the theatre or evenings out when I just need my ID, phone, and credit cards.
Daytime clutches never appealed to me unless they were small enough to be tossed in a tote or briefcase. I always used a clutch when I taught classes because I couldn't see hauling another bag around in addition to a tote or briefcase.
For daily on-the-go, though, I prefer a shoulder or cross-body bag so my hands are free. That's why my clutches are usually from places like Zara.
And, for the record, I never place my bag on the floor, or the table (was taught it was bad manners!), or on an unused chair in a restaurant. My bag is always snuggled next to my hip or on my lap. The only bag that I'll set next to my feet is my nylon travel tote or my briefcase. My pet peeve is to see people place suitcases on beds... Bags that are handled by others get set down in some really gross places.