Learning Proper Jazz Terminalogy?

[400$Bass]

Let's say an ensemble of jazz musicians play a song. The song originally was a Popular song which was recorded and the singer/lyrics were the focal point of the song. I'll use this for an example. Cole Porter wrote many songs. His songs were recorded by many famous singers. For the sake of this discussion..when an ensemble of Jazz musicians instrumentally play a Cole Porter song, using Jazz Techniques, is there a specific name for this type/style of Jazz?

An example would be as such: Oscar Peterson recorded an album where he played a batch of songs made famous by Frank Sinatra. I'm thinking the instrumentation was Piano, Bass, and Drums. What would that specific type of Jazz be called? Please respond.

[Damon Rondeau]

Those types of tunes are called standards. You'll sometimes hear people referring to "American songbook" tunes -- they're talking about standards. Not every pop tune sung by someone like Sinatra was a standard, but if you're talking Berlin, Gershwin, Kern, Porter, etc etc etc those tunes are indeed standards.

Improvising on standard tunes and swing rhythm are the DNA of jazz. You will hear jazz ensembles of all descriptions playing standards, in all kinds of styles. I would call the Oscar Peterson-type group of your example a straightahead piano trio. If the pianist played more like Bud Powell it might shade into the area of bebop....

[400$Bass]

Thanks for the clarification. Although I appreciate all of it...I prefer listening to Jazz where I know and am familiar with the melody/tune. Does that make sense....?