ELPH is a combination of the word 'elf' (for a camera that is small and "magical") and the word 'photograph.' In Europe, these are know as IXUS, and in Japan, they are known as IXY cameras. It's not really an acronym for anything.
The PowerShot A2500 is a 5x zoom camera, and the ELPH 115 is an 8x zoom camera. The original A series of PowerShot cameras were powered by AA batteries, hence the A designation, and were a less expensive version compact camera. The ELPH series were introduced before the A series, and have been generally a little more advanced and slimmer than the A series cameras. They were also more geared toward users who did not require all the manual controls that were found on the older A series cameras. The ELPH cameras were more of a "point and shoot" than the old A series. These days, however, there really isn't as much difference in the two series, and it appears that Canon is slowly phasing out the A series in favor of the ELPH. With the popularity of camera phones, the A series lack enough of an advantage over cell phone cameras to justify keeping them in the lineup.
