And, the .357 Magnum sounds like its smaller than the .38 Special, but, its not. They are both .357 in diameter. But, the .38 was named the .38 special, it sounded good.
Actually, it's kind of the other way around...well maybe.... .38 Special (full name is .38 Smith & Wesson Special) was based on .38 Long Colt, which in turn was the successor to .38 Short Colt. During the transition from cap & ball revolvers to metallic cartridges, the latter originally used "heeled" bullets that were the same width as the outside of the case, which was approximately .38". Although this changed at some point to non-heeled bullets with diameters closer to .36" (give or take, depending on the period), the name was kept (as was the .38" case diameter) and passed on to larger, more powerful cartridges (even with their slightly narrower bullets). I guess it wouldn't make much apparent sense to apply a smaller "caliber" number to something more powerful that is based on something weaker, right?
As for why .357 Magnum (actually .357 S&W Magnum, and based on .38 Special) was named as such, I would guess that it's because the "Magnum" part makes it sound powerful as it is, and that ".357" is not only the accurate diameter of the modern bullets (a personal preference of the inventor, perhaps?), but sounds cooler than ".38 Magnum" or ".36 Magnum".
Not to be confused with the 38 S&W. Or the 38/200.
Or even worse, .38-40 Winchester, which has .401" diameter bullets (mysteriously larger than the caliber name instead of smaller this time).
To the OP, the bottom line is that each so-called "caliber"--really the name of each type of cartridge--does not necessarily correspond to the real characteristics of the cartridge. Sometimes different characteristics are included in addition to the supposed bullet diameter, and sometimes those are obsolete or just plain inaccurate as well.
And as others have pointed out, some "calibers" have names based on different units (e.g. millimeters as opposed to inches), making direct numerical comparisons meaningless.
It's all pretty fascinating (I think) once you get over the initial confusion and learn to not take the caliber names too literally. You can start by familiarizing yourself with the most popular modern cartridges for handguns (since this thread is in a handgun section) before moving on to others. You probably know what they are, and even Wikipedia's information on most of them should be accurate (not 100% but close) and complete enough to get you started without getting too overwhelmed.