How does that first one work? The cap is a lower impedance path to ground and while charging the led is off then the cap discharges lighting the led then the cycle repeats? The transistor is chosen because of its voltage drop like a diodes?
By abusing the reverse breakdown voltage of the PN junctions. That one is quite low for these transistors. So once the capacitor charges up, the voltage across the transistor exceeds the breakdown voltage, that will rapidly discharge the cap (and make the LED flash once). The voltage drops below the breakdown voltage again because the discharged capacitor acts as a short at that moment - thus turning the current off. And the cycle repeats.
However, it is not the best circuit for something repeatable or robust.
The second one works because of special properties of that unijunction transistor being able to have the current reversed It acts as a NPN and PNP?
Unijunction transistor is a very obscure part, having little in common with regular transistors. The way it works is a bit complex, it is well explained here, for example:
https://www.electronics-tutorials.ws/power/unijunction-transistor.htmlBasically a relaxation oscillator - the transistor is off, the capacitor charges up until the turn on voltage is reached, the transistor turns on and discharges the capacitor again. And cycle repeats. Similar circuits have been done also with neon indicator tubes which have a similar behavior.
I'm finding these schematics online are just people drawings, and not tested in simulators or even in real life just "this seems like a good idea, my last circuit worked , so lets say it will work".
Hehe, welcome to the real world. Yep, that's very common, even circuits published in magazines and such.