I think there's been a lot of confusion generated herein, so I profer the following diagram which shows the various types juxtaposed with one another. Hope this clears things up.
Personally, I don't think the 20cm size are very practical.
Seriously though, my $0.02 worth is: be prepared to turn around. If the conditions are more extreme than you bargained for, high tail it out of there. I once was doing Mt Williamson in the San Gabriels. I could kick step up the mountain with the gear I had, but the snow had a heavy duty icy crust. Had I slipped, there would have been no way to stop without an axe which I didn't have. I turned around and climbed a much easier peak w/o ice. I might well not be here had I not.
Climbing straight up a steep slope in some ways is the more obvious case. It's when you're doing a traverse across a well trodden path. It looks safe because it's so well travelled, but if it's icy the day you do it, you really have to ask "what happens if I slip." Once you're off that small strip (the trail) of relative safety, you can be in for a world of hurt.
Think critically about your situation, and when warranted, live to hike another day.