For AC charging, the charger unit is in the vehicle - the 'charger' on the wall is just a box which switches the AC on and off, and has some other electronics to limit the rate of charging to some predefined values, plus various safety features.
Most vehicles have a single phase charger which is up to 7.2kW. Some have 3 phase which in theory is 22kW. Some vehicles may have charging devices which only support lower rates such as 6kW.
Most EVs use a Type 2 connector. A few older ones have the Type 1, which is electrically compatible with Type 2 so just needs a different cable - Type 1 at the car end, Type 2 on the other end.
For most, it's a cable with Type 2 on both ends.
For charging at home, the cable is normally tethered to the EVSE, as that's more convenient than removing and storing the cable each time.
If installing EVSE (what most people call a 'charger') then it's either a 7kW single phase if the location has single phase, or a 3 phase 22kW if the location has 3 phase.
Any car can plug into any outlet - if the car supports 2 or 3 phases and those are present, then they can be used. If not, only one phase is used.
A car with a single phase charger can be plugged into a 3 phase EVSE, but will only use a single phase and still only be 7kW maximum.
Charge rate also depends on the cable between the EVSE and the car, the state of charge of the car battery, temperature and other settings in the vehicle or EVSE which can limit the rate depending on external factors such as multiple units in a single location limited to a total power shared between them, or on the availability of local solar power, etc.
AC charging is intended to be used over a longer period at a low rate, typically when parked for several hours, or where the journey made to get there is relatively short, such as parking at a supermarket when shopping. Typical use cases are charging at home, when parked at work, when staying overnight at a hotel, at a gym, parked on the street, or anywhere else where the vehicle is likely to be parked for a few hours.
That's also why the nonsense about 'range' is mostly irrelevant - EVs are charged wherever they are parked regardless of how much range remains, rather than driving until nearly empty and then queuing up at Tescos on a Friday afternoon to refill.
DC charging uses the CCS connector, which is the same Type 2 connector with two extra connectors below it.
The large connectors are DC, and the smaller pins in the upper connector are used for communication between the vehicle and charger.
AC to DC conversion is done in the charger unit, which is why DC chargers are so large and expensive.
Charge rates go from 22kW upwards, and depend on the capabilities of the charger and what the vehicle can accept. Other factors such as battery charge level, local power availability and so on can all affect the actual charge rate obtained.
DC chargers always have a tethered cable.
DC charging is intended for situations where a large amount of energy is required in a short time, such as to add a couple of hundred miles when stopping at a motorway service station.
The only other variants are the Chademo connector for DC as used on some older Nissan and Renault vehicles - essentially obsolete now although most DC chargers still have it.
Early model Tesla vehicles misappropriated the Type 2 for DC charging with no extra pins, with the result that Tesla superchargers could only be used with Tesla vehicles.
However newer Tesla cars have the same CCS connector as everyone else, and they are refitting their Superchargers so that other vehicles can use them.
Those with the older Tesla cars can buy an adaptor from Tesla which converts CCS to the Tesla Type 2, so they can use any CCS DC charger.
but as electric cars on the road increase, we are likely to see people waiting their turn to charge cars when the car in front of them in the queue is only taking a ⅓ of charge available.
No, as charging an electric car is park, plug in, go do whatever you were there to do. There is no waiting around for anything - no one with a EV plugs in and then stands next to the vehicle for a couple of hours waiting for it to charge.
More public charge locations are certainly required, and eventually most parking spaces will have one.
This whole idea of 'queuing up' is what people with petrol and diesel vehicles do, because that's the only way of filling them with fuel.
It's also what everyone has been doing for the last 100+ years, and old habits are hard to get rid of - but EVs are not used in that way. For most of the time, it's charge little and often.