Then it is a soft wheel. A hard wheel would not have any resilience. No, some caster manufacturers use round tops, some flat - makes no difference. Correct diameter is determining factor for selection. Grip Rings expand when inserted in chair bases and hold caster in place in base.
Manufacturers stems vary.
Size or placement of grip ring not a factor. There is no metal notch in chair leg they have to fit into. They expand once stem is securely inserted into chair base. Wood clad have a wood or simulated wood cover, over metal thus a caster for metal bases must be used. However, soft black wheels made today should not mark.