English Translation
The students wanted us to help push the car.
The JP/EN pair doesn’t match.
- 学生たちは私たちが車を押すのを手伝ってくれた。= The students kindly helped us push the car.
- The students wanted us to help push the car. = 学生たちは私たちに車を押すのを手伝ってもらいたかった。
The first pair means that the owner of the car is US. And the students are helpers. The students actually helped. It’s done. くれた suggests that we appreciate their kindness.
The second pair means that the owner of the car is the STUDENTS. And it’s not clear whether we actually helped the students or not. The second pair can be used in the context of “the students asked us to help push the car on the street, but we had to decline in order not to be late for the meeting. So the students asked for help from other passengers.”