No, a Card doesn't have to be on a Playbook.
1. Creating a Card NOT on a Playbook
You can create a Card or a Playbook from anywhere in the app by clicking on the "+ New" button in the top right. Any time you create a Card from this button, it will not be associated to any Playbook. It will come up in search results.
If you go to All Cards Authored by You, you'll be able to see your Card and add it to the Playbooks that you want.
2. Creating a card on a Playbook
On a playbook's column, you can create a card by clicking the "+ New Card" option. By creating a card this way, the card will be on the Playbook:
Regardless of how you create a Card, you can always add it or remove it from a Playbook!