Buddha taught meditation to develop concentration, calm of the mind to finally experience nibbana.
Other religions (Hindu yoga, etc) also taught meditation.
So in which way Buddhist meditation is different? and leads to end of suffering? If I'm not wrong, if someone is absorbed in concentration, whatever religion does not matter. since there is no thought during absorption.
Please explain if possible in terms of 7 factors of awakening, 8 foldpath, etc...
The essential difference is that in Buddhist meditation, at some point one uses one's mind to actively examine and investigate one's direct experience and to realize it's nature that way. This is the seventh factor of the Noble Eightfold path, Right Mindfulness, Samma-Sati. It is described in the Sattipatthana Sutta like this:
"There is the case where a monk remains focused on the body in & of itself — ardent, >alert, & mindful — putting aside greed & distress with reference to the world. He remains >focused on feelings... mind... mental qualities in & of themselves — ardent, alert, & >mindful — putting aside greed & distress with reference to the world.
...
In this way he remains focused internally on the body etc... in & of itself, or >externally on the body in & of itself, or both internally & externally on the body in & >of itself. Or he remains focused on the phenomenon of origination with regard to the >body, on the phenomenon of passing away with regard to the body, or on the phenomenon of >origination & passing away with regard to the body. Or his mindfulness that 'There is a >body' is maintained to the extent of knowledge & remembrance. And he remains independent, >unsustained by (not clinging to) anything in the world. This is how a monk remains >focused on the body in & of itself."
(Source: http://www.accesstoinsight.org/tipitaka/mn/mn.010.than.html )
The result of which is that the mediator begins to discern that reality is impermanent, unsatisfying, and non-self. As one realizes this more deeply, one is lead to liberation. This process is described in many places in the Suttas, most famously in the Anatta-Lakkhana Sutta like this:
"Seeing thus, the well-instructed disciple of the noble ones grows disenchanted with >form, disenchanted with feeling, disenchanted with perception, disenchanted with >fabrications, disenchanted with consciousness. Disenchanted, he becomes dispassionate. >Through dispassion, he is fully released. With full release, there is the knowledge, >'Fully released.' He discerns that 'Birth is ended, the holy life fulfilled, the task >done. There is nothing further for this world.'"
(Source http://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.059.than.html )
Non-Buddhist systems of meditation often focus on just developing concentration without this process of analyzing direct experience, and so end up attaining other things, such as mastery of the Jhanas, rebirth into the Brahma worlds etc... There is nothing wrong with these other things, and they can also be a part of Buddhist practice, but they aren't the goal.
This is one of those questions that an entire book could be written to answer. Fortunately it already has - the Meditative Mind by Daniel Goleman. The book is a comparative survey of mediation across a number of traditions. He takes in Buddhism and Hinduism which one might expect and also brings in Christainity, Judaism, Islam and secular practices.
This book doesn't give any particular pride of place to Buddhist practices as such although he does reference the Visuddhimagga extensively as a map to meditation. So maybe it is overall looking at it in a Buddhist framework although I think it is more fair minded than this.
If I had to maybe try to give the main difference I would perhaps say there is a real systematisation of the path to enlightment that is perhaps not as strongly pronounced in other traditions particularly if we are looking a Abrahamic faiths. This is probably best exemplified by the 51 mental factors as outlined in the Abididarma and also in maps in the aforementioned Visuddhimagga.
I think there is also a feeling that Buddhism has emphasis on insight practices but not been an expert in comparative religion I couldn't attest to that. Certainly in the Meditative Mind there is a list of awakened states and this is not exclusive Buddhist at all. Sufism has Baqa, kabbalah has devekut, TM has cosmic consciousness etc...
The method of meditation is learning through play. You study your mind by trying to make it do things. As you study the mind, you study various aspects of how it generates "reality".
For example, if you are drowsy, by trying various mental tricks that might keep you awake, you can learn something about your mind. (I'm not suggesting staying up as a serious practice, just using it as a simplest example.)
Some people erroneously take the goal of meditation to be a state of non-distraction (from the object of meditation, e.g. breath), or even a state of open awareness -- which is pretty cool, but not the goal. The goal is to exhaust samsara. In order to exhaust samsara you must exhaust ego. In order to exhaust ego you must explore all corners where Enlightenment might hide, until you know you couldn't have possibly missed it. Then it finds you :)
Try to see this book..knowing and seeing...
http://www.buddhanet.net/pdf_file/know-see.pdf
This book is a practical version of The Path of Purification. This book is also a very good reference.
May of the other systems outside Buddhism do not emphasise Morality, Concentration and Wisdom (3 Fold Training) to the extent there is in Buddhism. In many cases it become to develop either morality or concentration. For enlightenment you need all 3 hence Buddhism is the only holistic and balanced systems as per my perspective which can take you to enlightenment.
In buddhism you use meditation and concentration as a tool to see reality as it is. This includes understanding of the Dependent Origination, the 3 Characteristics, and the 4 Noble Truths.
When practicing Vipassana and start developing the 37 Factors of Enlightenment which include the 7 Factors of Awakening and the 4 Right Exertions you more towards enlightenment.
