The question is in the subject.
In this link are various water heaters we have here in Israel (Including gas and electric): https://www.zap.co.il/models.aspx?sog=h-waterheater
They are popular at barber shops, but rarely used at the homes.
Are these considered "Electric showers"?

As far as I am aware, the term "electric shower" refers to a shower head with a built-in heating element to make hot water for your shower, but I don't live in any areas where this is done so I don't know for sure.

"Electric shower" in google, lead to similar results for "מחמם מים" (Water heater) in Zap: Link1 , Link2 .

I think of The Showerhead of Doom when I read electric shower, BUT if it's an immersion heating element inside a tank that's directly connected to a shower (single piece) then it would count as an electric shower to me. It's basically a big kettle if you think about it, only used to take showers.

The most (in)famous are south american (there's more than Brazil) ones, they just install that because houses don't have a boiler room or a gas line, yeah there are electric boilers or water heaters (not the same) but you still need the physical space and all the plumbing, valves, etc. so what they do is build the house with a single line for cold water rather than two, and it's plastic not copper, not rated for hot water.
Same with gas, only fancy houses have gas plumbing installed, the rest have a propane tank with a flex hose for the cooker, you'd need another one to run a heater and it'd probably empty it in a matter of days.

My house has plumbing and a boiler but it's ancient, if you wanted to build something like this today it'd probably cost millions due to all the labour and materials, copper pipes were dirt cheap 140 years ago vs. today and you 100% needed them if you wanted your house to have a bathroom, plus you also needed pipes for lighting, as it was gas, candles and portable lanterns were a thing of course but gas is where it was at.

This looks to me like any water shower connected to an electric tank with heating element is an electric shower.

I think the distinction between a water heater and electric shower would be that in the case of the electric shower, the heating element heats water for the shower and nothing else.  In the case of a water heater, it provides central hot water to other appliances and fixtures along with the shower.

Tankless heater supplying straight to the shower or integrated with the shower

In Israel the Atmor company ones are the most common, which became a generic name for all of them. The proper (and little known, rarely used) Hebrew term for the technology is חימום עובר - "passing heating" or "transient heating"