There are two categories: active and passive skills.

Active skills are the ones you use during battles, while passive ones enhance the active ones.

In the following screenshot, the passive skills are locked as they require a specific character upgrade:

As you can see, the Fox Fire skill is the normal one when you connect same color runes. The Blow Kiss skill is the special ones that appears after you connect at least 3 runes.

Skills can be leveled up by spending coins, in order to make them more powerful.