It's very similar, just different techniques. Mindfulness meditation is generally a western, scientific way of describing it after university researchers began studying the practices of Buddhist monks, and perhaps other types too like Hindu priests.

There are many techniques, just keep an open mind and explore which one works best for you. Don't be judgemental on which is 'better' than the other as this would be counterproductive, just realize that some may be more suitable for you personally.

While there are many, in general you can start your search on the topic by googling the following:

Loving Kindness Meditation (Metta) by Matthieu Ricard
MBSR by Jon-Kabat Zinn
MBCT by Mark Williams
Headspace by Andy Puddicombe