is the method of playing acoustic guitar and classical guitar the same?
The technique is different. Technically both are acoustic guitars since neither uses amplifications. The left hand is basically the same, the right hand is different. Classical guitar is usually played with the fingernails and has nylon strings at lower tension, whereas acoustic is typically played with a pic and usually has steel strings at higher tension.
A classical guitar is a type of acoustic guitar. What you’re simply calling an "acoustic guitar" is more properly referred to as a "steel string acoustic guitar" It’s also commonly called a "folk guitar"
Both are unique instruments with very different sounds. Those different sounds compliment different styles of playing, those styles call for different techniques.
There are similarities, but there are also some unique differences. Something like this: http://www.youtube.com/watch?v=Avti498yW5Y wouldn’t work that well on a steel string acoustic. However, something like this:http://www.youtube.com/watch?v=4P9mmZyGb4s wouldn’t work on a classical guitar at all.
Another notable type of acoustic guitar that most people are unaware of is the flamenco guitar. Most people simply think that any nylon stringed acoustic is a classical guitar, but that is untrue. The flamenco guitar has some very notable differences in construction that make it more appropriate for flamenco and other types of acoustic guitar music.
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The technique is different. Technically both are acoustic guitars since neither uses amplifications. The left hand is basically the same, the right hand is different. Classical guitar is usually played with the fingernails and has nylon strings at lower tension, whereas acoustic is typically played with a pic and usually has steel strings at higher tension.
References :