Checkboxes and radio buttons should be used in very different ways in a user interface.

A checkbox is for selection. Checking demonstrates inclusion.

Radio buttons are for a mutually exclusive choice. When you have 2,3 or maybe 4 options to choose from, use radio buttons.

A checkmark should not be used for a selection where being unchecked is not obvious. For example, one product I reviewed had http as a checkbox. So if you checked it you got http and if unchecked? Https? Ftp? What?

Radio buttons should not be used if you have more than 4 items. In that case, use a drop-down list.

In structuralism, a binary opposition is seen as a fundamental organizer of human philosophy, culture, and language. -wikipedia