Moving someone to somewhere by a vehicle

In English ,there are different ways that someone can use to say how he or she moved someone freely by a vehicle to a place:

1- To give someone a ride to somewhere
An expression which is more commonly used in the U.S.

- He gave me a ride to the airport.
- My brother gave me a ride to my house on his motorcycle.

2-To drive someone to somewhere
It is used in both American and British versions.

- Her daughter drove me to the airport.

3-To take someone to a place
It is also common in both American and British versions with a subtle difference in meaning.It mostly means she/he accompanied me to the station/airport....For example, if I didn't know where the station was he could have gone with me on the bus.

- His brother took me to the airport.

4-To give someone a lift to a place
It is more common in the British dialect ,though it is used in the U.S. less commonly.

- He had a car and gave/offered me a lift to the airport/a lift home.

5-To run someone to somewhere
An informal expression which is used in the British dialect.

-Would you mind running me to the station?

The five expressions suggest a brief journey, often provided as a favor. The destination would usually be a building or amenity, rather than a town, etc.
For longer journeys, you can add "down" and "up",to "run" depending on the geographical relation:

1. My cousin ran me down the river last week.
2. He thought I would run him up to New york.

For journeys between nearby residences, offices, etc., you can use "run over":

3. I was going to run them over to the museum.
4. Why didn't you run your brother over to his work?

So, all of them have the same meaning except took which doesn't (necessarily) specify that a car was involved - though it may have been.