Can you actually get different tariffs in the UK for residential?

In Canada most of that is pretty opaque. Electricity tariffs are not really something that most households would worry about. Businesses and Industrial usage do though

Yes, there are multiple competing providers - all the electricity comes from a single grid but competition in how you are billed for usage.

Many people choose a single fixed or variable rate tariff, but there are also off-peak tariffs that are very cheap at night but slightly more expensive in the day (designed for EV users), or even tariffs where the rate changes every 30 minutes depending on what is being generated - in this case when there is excess solar and wind generation then sometimes the rate even goes negative and you are paid to use the excess power.

Yes, the newer suppliers have EV and solar friendly domestic tariffs. Plug it in overnight, and the supplier determines when the charge happens and charges at the reduced rate.

A simple day and night tariff was introduced at some point in the 1980s in the UK.

Most places I lived had this set up.

(Nowadays smart meters offer many more options.)

Sure

You can base it on the wholesale price, great if you have battery storage

https://octopus.energy/smart/agile/

Or just an overnight rate

https://octopus.energy/smart/intelligent-octopus-go/

Again if you put in a £5k 10kWh battery you are golden, as you put 8kWh into your car and 8kWh into your battery every night, dropping your electric cost to £38 a month (plus the standing charge, which is far higher)