difference between in the back and at the back

There is a little garden in the back of the house.
This means that there is a garden actually INSIDE the house.
You may hear this sentence, but the speaker is actually meaning:
There is a little garden in the backyard of the house.

The sentence should be:
There is a little garden at the back of the house.
A house has a front, sides, and back. The little garden is located at the rear of the house, (adjacent to the back of the house.)
'at' is used to give the general location of something. 'in' and 'on' are specific locations.


There is a vehicle logo in the back of the car.
The logo is on the back seat of the car?
There is a vehicle logo at the back of the car.
This is too general. We don't know whether it's in the boot, on the bumper, or being pulled along on a piece of string.
We would say:
There is a vehicle logo on the back bumper of the car/on the back window of the car.

There is a trunk (boot) (in/at) the back of the car.
Either is possible, because everyone knows what a trunk (former British term for the storage area, but we mainly say 'boot' now) is.