Jazz has been around long enough for there to be many cases of musicians sharing the same name: there was a bassist named Billy Taylor, who, most famously, played with Duke Ellington, and who had a son named Billy Taylor Jr., neither of whom was related to the pianist and jazz spokesman Dr. Billy Taylor Jr.

In addition to the pianist Bill Evans, who worked with Miles Davis, there is a fusion-oriented saxophonist named Bill Evans, who also worked with Miles Davis, and, coincidentally, the famous saxophonist and composer Yusef Lateef, before his conversion to Islam, worked briefly under the name Bill Evans. The swing era gave us both a tenor saxophonist (who worked with Jimmie Lunceford) and a trumpeter (who worked with Benny Carter and Fletcher Henderson) named Joe Thomas, who were both born in 1909. It takes a Phil Schaap or an Ira Gitler to sort it all out.

But who would have thought that the comparatively smaller world of Israeli jazz would be capacious enough for there to be two youngish musicians both named Avishai Cohen, born seven years and 34 miles apart? Is that moniker somehow the Hebrew equivalent of Bill Evans or Joe Thomas? Not only are both Avishai Cohens currently active, they both have new albums out, and are both working the local and international club and festival circuit, to the confusion, one imagines, of bookers and promoters. Surely it’s more than a Cohen-cidence.

The bassist Avishai Cohen, who was born in 1971 in Jerusalem, is best known for his extended stint with piano superstar Chick Corea. In addition to touring and recording extensively with Origin, Mr. Corea’s acoustic trio, from roughly 1997-2002, Mr. Cohen also recorded his first four albums as a leader for Stretch Records, Mr. Corea’s personal imprint within the Concord Records family. Since then, he has released an additional five CDs on his own Razdaz label, distributed in conjunction with Sunnyside Records, and now the new “As Is … Live at The Blue Note” on Half Note, the label operated by The Blue Note jazz club. (Coincidentally, there are two jazz operations based in New York called “Blue Note,” the record company and the club, which have nothing to do with each other.)

The trumpeter Avishai Cohen was born in Tel Aviv in 1978. Although his current release, “After the Big Rain” (Anzic) is only his second as a leader, following a 2003 release on the Spanish label called “The Trumpet Player” (presumably named thus to distinguish this Mr. Cohen from the bass player), he has worked and recorded a lot with his siblings, the saxophone players Yuval and Anat Cohen, in such groups as The Three Cohens and Waverly Seven. He debuted the music from that album in an excellent set last Thursday at Joe’s Pub.

The two Mr. Cohens play very different instruments, have very different backgrounds, and the music of one could not be confused with that of the other, yet they have a lot in common. The music on both of their new projects is very world-y, which is hardly surprising for two multi-cultural musicians who were born and raised in Israel before becoming part of the New York jazz scene. They both use American jazz as a foundation for a music that includes elements from at least three distinct parts of the world: the Middle East, Africa, and Latin America.

The bassist’s new release is actually a double-disc that contains an audio CD and a DVD, both taped at The Blue Note last October. The group is a quintet, co-starring trumpeter Diego Urcola, pianist Sam Barsh, drummer Mark Guiliana, and also the excellent saxophonist Jimmy Greene, a fine multi-reed player who makes any ensemble more interesting. On “Smash,” which is heard on both discs, Mr. Cohen plays electric bass, on which he says (in the liner notes) his main inspiration was the late Jaco Pastorius, Mr. Barsh plays electric keyboards, and Mr. Greene plays soprano. The combination of those sonic textures and the piece’s funky rhythm gives the whole thing a feeling very much like smooth jazz; however, the challenging nature of the improvisations pretty much removes the smooth elements. “One For Mark,” apparently dedicated to the drummer (there’s also “Samuel” for the pianist), begins with a rhythm pattern on the piano that sounds straight out of Havana, but keeps developing into an unpredictable, international direction. “Feediop,” is one of those funk grooves so prevalent in contemporary jazz, which purport to make the music very basic and simple, but which, in actuality, can only be properly counted or danced to by a Juilliard student with a metronome in his back pocket.

Both discs conclude the same way, with a slow ballad for acoustic bass, piano, and drums titled “Remembering,” which contrasts a complex semi-classical piano line (a love child of Beethoven’s “Für Elise” and “The Godfather Theme”) and a comparatively simple, emotionally direct bass part. This is a lead-in to the finale, an electrified, punked-up treatment of the Ellington standard “Caravan,” a tune describing a desert journey that apparently has special relevance for a Middle Eastern jazzman. The melody is phrased in unison by Mr. Greene’s soprano and Mr. Barsh on melodica, a wind-driven mini-keyboard, the sight of which is a highlight of the DVD.

As he announced at Joe’s, the trumpeter Avishai Cohen’s “After the Big Rain” is the third part of a trilogy of recordings (the two prequels have already been recorded but not released) depicting the story of creation in music, making the trumpeter the third contemporary musician that I know of, after Stefon Harris and Randy Sandke, to address Genesis (the book, not the band) in jazz terms. The featured presence of the brilliant Benin-born guitarist and vocalist Lionel Loueke gives the proceedings a much more African vibe. Instead of the pop feeling occasionally evident on the other Mr. Cohen’s album, the use of African rhythmic patterns and drums makes certain pieces, like “Meditation On Two Chords,” sound more like ambient music. However, the next track, “African Daisy (Le Suite African)” shows the more extroverted and forceful side of both African music in general and of Mr. Cohen’s trumpeting. A longish, 11-minute piece with generous spots for Mr. Loueke and the others, “Daisy” reaches its climax with a dynamic solo from Mr. Cohen, trumpeting over this outer-worldly blend of percussion and electronics, a sequence that’s both sonically and rhythmically compelling at the highest level. As intriguing as the background may be, the best moments are on those tracks, like “Daisy” and “Parto Forte,” where Mr. Cohen makes it clear that context is not everything, where he just cuts loose and wails, without particularly caring whether he’s accompanied by a swing band, a bebop rhythm section, or an intercontinental electro-acoustic Afro-Caribbean ensemble. There’s nothing on the disc that’s as important as his own aggressive improvising.

Both of these musicians are well under 40, and it’s easy to imagine them making a vital contribution to the international jazz scene for a long time to come. Who knows? If I thought that I had any musical talent, I might also start working under the name “Avishai Cohen” just to get a piece of the action.