As the other answers point out the Real Book is just a collection of lead sheets.

You must be just starting out with jazz so you should look at both:

• Fake books and lead sheets, and get some books or lessons about how to play from a fake book. There are lots of lessons for that.
• Jazz transcriptions, which is when someone writes down in notation a recorded jazz improvisation.
• Original published sources. Depending on the song you can get the original music many standard songs come from Broadway musicals.

My personal peeve was with rhythm changes and the song I Got Rhythm. There literally is no one definitive version of rhythm changes. There are endless examples of the changes and lead sheet versions. I finally got a copy of the Gershwin music from a published copy of the musical Girl Crazy. But, even that was surely not the notation pages used by the orchestra for the original production. It was just a piano reduction. You can also find various piano solos which are probably the work of various editors/arrangers and not necessarily a transcription of anything Gershwin played himself!

Eventually you realize this kind of music - jazz and pop music - is not about a definitive score. I suspect many famous tunes started as some combination of notebooks, band charts, etc. used to make a first recording and those sources are not published. Then some sheet music version was published for people to play at home, either to promote the tune or to meet demand for a popular tune. Other musicians perform and record the tune. In jazz the first fake book was developed and people wrote lead sheets that sketched a general outline of songs.

There is no "urtext" like in classical music. You need to look for the resource that fits your purpose...

how can I practice in a way that is more similar to their music?

• get some resources about how to play from a fake book, you don't simply play the lead sheet exactly as written
• look for transcriptions of specific performances you like

One final thought. You tagged your question with guitar, but compared the fake book to Paul Desmond recordings. You will probably have an easier time learning how to play guitar from a fake book if you compare to recordings or jazz guitarists.

As the other answers point out the Real Book is just a collection of lead sheets.

You must be just starting out with jazz so you should look at both:

• Fake books and lead sheets, and get some books or lessons about how to play from a fake book. There are lots of lessons for that.
• Jazz transcriptions, which is when someone writes down in notation a recorded jazz improvisation.
• Original published sources. Depending on the song you can get the original music many standard songs come from Broadway musicals.

My personal peeve was with rhythm changes and the song I Got Rhythm. There literally is no one definitive version of rhythm changes. There are endless examples of the changes and lead sheet versions. I finally got a copy of the Gershwin music from a published copy of the musical Girl Crazy. But, even that was surely not the notation pages used by the orchestra for the original production. It was just a piano reduction. You can also find various piano solos which are probably the work of various editors/arrangers and not necessarily a transcription of anything Gershwin played himself!

Eventually you realize this kind of music - jazz and pop music - is not about a definitive score. I suspect many famous tunes started as some combination of composer's notebooks, band charts, etc. used to make a first recording and those sources are not published. Then some sheet music version was published for people to play at home, either to promote the tune or to meet demand for a popular tune. Other musicians perform and record the tune. In jazz the first fake book was developed and people wrote lead sheets that sketched a general outline of songs.

There is no "urtext" like in classical music. You need to look for the resource that fits your purpose...

how can I practice in a way that is more similar to their music?

• get some resources about how to play from a fake book, you don't simply play the lead sheet exactly as written
• look for transcriptions of specific performances you like, the traditional jazz way is to do it by ear, "quote" parts of their playing or emulate it in a general sense

One final thought. You tagged your question with guitar, but compared the fake book to Paul Desmond recordings. You will probably have an easier time learning how to play guitar from a fake book if you compare to recordings or jazz guitarists.