While superficially, Buddhist meditation looks like yogic meditation, the two are actually quite different. They both are based on very different philosophy, have a different purpose, and result in a different effect.
Generally, Westerners who practice "Eastern" meditation are trained in one of the yogic varieties of meditation, unless they have expressly studied under a Buddhist teacher. For example, Robert Monroe's hemisync has similar effects as yogic meditation. Similarly, New Age tends toward the yogic style of meditation.
I have studied both. First, I was trained in the yogic meditation by a Moravian yoga teacher who was a direct student of an Indian swami (whose name I forgot, sorry--hmmm, Vivekananda?). I studied under him in the early 1970's. It made a big and positive difference in my life. It also made practicing Buddhist meditation much harder later on.
I now practice Buddhist meditation, though I sometimes slip back to yogic meditation--unfortunately.
The difference between the two types of meditation can be best described by the result of some medical research mentioned by my Zen teacher. I do not know who exactly did the research, as I only learned about it second hand from my Zen master.
Anyway, he said the researchers used three groups of subjects for their experiment. One group was trained in and practiced yogic meditation. Another group practiced Zen meditation, which is a type of Buddhist meditation. The third group was the control group which consisted of a random sample of people who did not practice any type of meditation at all.
All subjects were connected to an EEG machine (i.e., an electroencephalograph - the machine that graphs brain waves), and were asked to meditate in a quiet room. At random intervals some kind of sound was produced (I think it was a brief electric bell sound). Not surprisingly, the three groups showed quite different results.
The control group showed random results. That is to say, their brain waves went up and down randomly all the time. Their minds were busy all the times, they did not quiet down. They reacted to the sound differently every time. Sometimes their waves got into a big amplitude, sometimes a smaller one, depending on whatever was going on inside their minds at the time.
The yogic group had very low amplitude: They were truly meditating, emptying their minds from everyday concerns. When the bell struck for the first time, their amplitudes peaked momentarily: they noticed the sound. However, the second and subsequent times, their waves remained of low amplitude. That indicates they "turned off" the sound in their minds and simply ignored it.
The Zen meditators were equally quiet. Their amplitudes were low, showing that their minds were not wondering around. In that regard, they were the same as the yogic meditators. When the bell struck the first time, their waves peaked, just like the yogis. Unlike the yoga group, the Zen meditators peaked at the second strike, and all other strikes of the bell. Their reaction was the same the first time and every other time: They noticed the bell, then continued meditating.
The thing the yogic meditation and the Buddhist meditation have in common is that their practitioners quiet their minds. When there are no external stimuli, there is no internal disturbance (unlike the control group).
The difference is in the reaction to external stimuli: The yogis turn them off as distractions. The Buddhists pay attention to them every time, but only while they last. In other words, they notice them, register them if you will, then return to quieting their minds instantly.
This difference is due to the differences in philosophy, the differences of the why of meditation, the purpose and goal of meditation (and the appropriate differences in training and practice).
The purpose of yogic meditation is to turn off all distractions, to get into a state of deep relaxation, turning off the external world, and quieting the internal mind.
The Buddhist meditation has a different goal. It, too, turns off internal distractions, it quiets the mind, stops it from wondering aimlessly. In that regard, both types of meditation are identical (and very beneficial). However, the Buddhist meditation does not turn off the external world, it continues paying attention to what is happening in the surroundings, but only while it is happening.
As I said, both types of meditation are very beneficial to their practitioners. I am certainly not saying one is better than the other, I am just saying they are different.
The Buddha emphasized awareness. He said that no matter what we are doing, we should be aware of what we are doing and how it affects us. From the Buddhist perspective, awareness is the key to awakening (or enlightenment as some like to call it). We need to be aware at all the times, that includes the time we are meditating. Indeed, the increase in awareness is the purpose of Buddhist meditation.
We quiet our minds not just to relax but to observe and to observe better. We observe what is happening around us. We observe what is happening inside us. We only observe it while it is happening. We do not dwell on it once it is gone: We do not analyze it. We do not categorize it. We do not speculate about it. We do not form theories about it. We simply observe it, are aware of it.
It is the essential Buddhist belief that analysis, categorizing, theorizing, is what keeps us all distracted from reality. Doing that keeps us in a world created by our minds, a world that is not reality but concept. It is only through observing what is, through pure awareness that we can come to true understanding of the reality that is as it is, and eventually awaken from samsara--the world of delusion that is created by our minds and only exists within our minds.
For a Buddhist the whole purpose of sitting in meditation is to create the state of mind that is awareness of the world around us and the world within us, and to keep that state of awareness even after we stop sitting. In other words, to meditate always, 24 hours a day, seven days a week, always, always, always.
That is not to say we are always successful--if we were, we would already be awakened (we would not be Buddhists, we would be Buddhas). But at least that is our goal.