Indeed. The first is blindly following a dogma, the second is true knowledge.
An example: I have been taught to never attempt shifting the gear in a car before pressing the clutch. I accept this as a dogma, but I have no idea what would have happened had I tried really hard. When I asked "why", the only answer I got was roughly "the engine would break". Only some car mechanics / engineers have enough understanding to explain in detail what would have happened. They have knowledge, I'm following a dogma.
Actually, with enough experience with a given vehicle, it is quite possible to smoothly shift it without the clutch. When the engine reaches the appropriate RPM, you let off the gas as you take the car out of gear, smoothly and firmly shift to the next gear at the right time (a super-narrow window), and ease into the gas again. Unfortunately, if you get any of that wrong, you get an unpleasant (and somewhat damaging) grinding.
Your transmission is a series of gears with varying ratios of wheel revolutions to engine revolutions. When you upshift, your engine requires fewer revolutions to drive your wheels. When the no-clutch-shifter lets off the gas, the engine's RPM begin to fall. With the correct timing, the shift is performed during this drop in RPM such that the engine's current RPM matches the RPM necessary to drive the car at this speed in this new gear. This obviates the need for a clutch, since the engine and the rest of the drivetrain (for which the transmission is the link) are being manually synchronized: the shift is performed with a technique that keeps everything spinning at the same relative speed.
When you depress the clutch pedal, the transmission disengages from the engine, allowing you to freely shift without regard to the engine's machinations. When you let out the clutch, what typically occurs is that a carbon disk slips a bit before fully reëngaging, allowing the engine and the rest of the drivetrain to gradually synchronize. This is the "catch" that you feel when you let out the clutch.
To illustrate explicitly, let's say we're shifting from 3rd gear to 4th gear at about 30 MPH, and for this car at 30 MPH the engine must spin at 5000 RPM in 3rd gear and 3000 RPM in 4th. Without the clutch, you left off the gas and pull the car out of gear (taking it out of gear is a split-second after letting off the gas), the engine's speed (RPM) begins to fall as you pull the shifter into 4th, and just as the engine hits 3000 RPM (on its way down to 1000, the idling rate), you shift the transmission fully into 4th gear. With the clutch, you jam the clutch and shift, and the engine could be anywhere from 1000-4500 RPM when you let the clutch back out. The clutch slips a bit, allowing the engine to reach the appropriate 3000 RPM before it is fully engaged. Without the clutch, you have very little room for error.
IANACM, but I think car mechanics have a model in their head about the gears and rods that make up the shifter, but they certainly don't know off the top of their head which exact gear will break or bend when you try shifting from 2nd to 3rd in a 1990 Ford Focus.
I also ANACM, however I can guarantee you that it is impossible for any gear to break or bend under those conditions (the first model year for the Ford Focus was 1998).
Regarding such 'trivia that might come in handy one day', it is possible on some cars to shift gears without using the clutch, but you have to get the timing exactly right.
If you time it right the shift will happen from say to 2nd to neutral at one rpm (to neutral is always possible without the clutch), then you reduce the rpm until you know it will match 3rd gear for that speed (good hearing helps here) and then you can make the shift from neutral to 3rd without any force at all. The more 'sloppy' a gearbox the easier this goes.
As long as you don't force things you'll be fine, if you do force it you'll likely be greeted by expensive grinding noises.
On the classic 'beetle' and 'mini' engines I can do this without fail or any chance of damage.
Modern cars (read more expensive) I haven't tried.
Of course this is not what you're supposed to do but it's interesting when you have a 'junker' to play around with it until you can do it right.
