I have been reading about volts and about the water pressure analogy being inadequate to describe electricity, since pressure makes water increase speed and thus would mean electrons would also have an increase in speed under a larger potential, So if an electron doesn't increase in speed or have a greater kinetic energy under a larger volt, and it always carries the same charge, and current is the number of electrons passing through a point: How is one amp under 1 volt even different from 1 amp under 2 volts?
If 2 volts produce 1 amp of current, there must be a higher electrical resistance than in the case of 1 volt producing 1 amp of current.
Using your water analogy, you have increased the pressure but also added rocks which slow the water down.
This is the analogy I think of (No, not the water pressure one) but I only took a couple intro physics classes in college so please correct me if this analogy is completely off..
If voltage is the energy difference between two points and amperage (ampere?) is the number of electrons traveling between these two points then we could think of it as a deep well that we are dropping rocks down.
Increasing amps means we start dropping bigger rocks down this well. Increasing volts means the well gets deeper.
This analogy gives you an intuition about why static electricity (high voltage, low amps) is isn't dangerous: imagine throwing a handful of sand down a super deep well.
Also, you can apply it to situations of low voltage & super amps ie if we connected 1000 mostly dead batteries in parallel: imagine a huge boulder hovering a centimeter off the ground, it'd kill you if you got under it but that won't happen easily (but it might destroy your finger).
In your situation, it's the same size rock being dropped but there's a greater energy difference between where it is and where it will be when you release (discharge) it.
The answer from @Benitok is nicely short and good, but it seems you still have some doubts. Allow me therefore to give my take on an explanation.
How is one amp under 1 volt different from 1 amp under 2 volts?
It isn't. 1 amp of current is 1 amp of current. But it can of course be produced in different ways. Which might cause more heat waste or other energy loss. But 1 amp is 1 amp nevertheless.
Think about your shower tap. During the years it clogs with chalk. Less water comes through. The water pressure didn't change, but less water comes through now that the resistance against the water flow is higher. To still get the same water out, you will have to turn up the tap and increase the water pressure. In this way different pressures can give the same amount of flow - simply because of different resistances along the way.
What in this way happens along the way in order to create a specific flow can vary. Same for electric circuits. The big difference here is just, that even through the current is the same, more waste heat might be produced depending on how this current is made. (Higher voltage increases the power release)
1 amp under 1 volt, that is an expression like 1 car under 1 m water, doesn't make sense.
1 amp is a flow of a particular number of electrons through an electrical leading circuit. At every location of this circuit the flow is equal to all other points. Compared with water, it is a particular amount of water circulating in e.g. a closed tube circle.
Of course, the water will not circulate in a closed tube circle at all, it will not move at all. The same is with electronic circuit from e.g. a close wire circle. The electrons will not move at all. There will be no current, no amps.
If the water should move/circle, we need a water pump, for electrons we need a electron pump. An electron pump is e.g. a battery.
Unfortunately the tube is a flow resistance for water, the leading wire has a flow resistance for electrons. When we start a flow and stop the pump, the water will not continue flowing, the electrons will not continue flowing, they will stop flowing because of the resistance, sooner or later.
We can measure the flow resistance of a tube as well as of a electric leading material. For a water tube it is measured in pressure per amount of water flow, and for electric leading material it is measures in Volts per amount of flowing electrons, that is flowing amps.
Volts is the unit for pressure. Amps is the unit for flow of electrons, that means amps.