In layman's terms (ie, off the top of Mark's head) ...
First you've got the software package, ASE, ASE/CE, REPserver, SDK, etc
Then you've got the software version, eg, ASE 15.0.3, ASE 15.5, ASE 15.7, ASE 16, REP 15.7.1
Then you've got a patch level, eg, SP63, SP111, SP121
NOTE: ESD## is the old Sybase patch level (eg, ESD2, ESD5) and has been replaced with SAP's patch level designator SP###
The EBF is typically a unique, ever-increasing number assigned to a combination of software package, version #, patch level and OS platform. For example, ASE 15.7 SP121 has been released for several OS platforms (linux 64bit, Solaris SPARC 64bit, Solaris x86 64bit, etc) so you'll find several downloads for ASE 15.7 SP121 with a different EBF related to each of the supported platforms. An EBF number should relate to a unique download file (out of all possible Sybase software downloads).
As for your questions ...
The easiest way (for me) to keep track of the ASE SP(2-digit) and SP(3-digit) codes ... these are 2 different code paths, with the 2-digit series being an older code path with new code releases representing (mostly) bug fixes ... while the 3-digit series is a newer code path with new code releases representing new features as well as bug fixes.
NOTE: The 2-digit and 3-digit paths are currently active, ie, we continue to see new releases for both code paths (hence what looks like conflicting release dates if comparing a 2-digit release to a 3-digit release); as long as you compare 2-digit releases to 2-digit releases, and 3-digit releases to 3-digit releases, you should be fine.
In your case you're running ASE/CE 15.7 SP111 EBF22865 (ie, a 3-digit release, so ignore the 2-digit releases). So from an upgrade perspective you're looking for 15.7 a) SPXXX where XXX > 111 and b) EBFYYYYY where YYYYY > 22865 *AND* refers to the same OS version that you're currently running on (eg, Solaris SPARC 64bit).
Obviously (?) you could also look at ASE 16 (if available for ASE/CE) in which case you're likely looking for the larges SPXXX with an EBFYYYYY where YYYYY > 22865 *AND* refers to the same OS version that you're currently running on.
Clear as mud? ;-)