Do I have to become a Buddhist?
No. Some meditators consider themselves Buddhist and some don’t.
What kinds of meditation are there?
In general, there are two kinds: focusing meditation and insight meditation.
In a focusing meditation you choose one object and work with that object;for example, repeating a mantra or focusing an image (real or imagined, excluding all other experience. This practice develops steadiness of mind. Transcendental Meditation is a well-known example. Metta practice is also a focusing practice.
Insight practice is not, but it relies on the ability to steady the mind in this way, focusing is one aspect of a part of mindfulness. The short-term after-effect of focusing practice is feeling relaxed.