split cache used when processing different split
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I was not able to reproduce this behavior (I tried without using pytorch lightning though, since I don't know what code you ran in pytorch lightning to get this).

If you can provide a MWE that would be perfect ! :) Hi, I think the issue happened because I was loading datasets under an `if` ... `else` statement and the condition would change the dataset I would need to load but instead the cached one was always returned. However, I believe that is expected behaviour, if so I'll close the issue.

Otherwise I will try to provide a MWE
## Describe the bug`
```
ds1 = load_dataset('squad', split='validation')
ds2 = load_dataset('squad', split='train')
ds1 = ds1.map(some_function)
ds2 = ds2.map(some_function)
assert ds1 == ds2
```
This happens when ds1 and ds2 are created in `pytorch_lightning.DataModule` through

```
class myDataModule:

    def train_dataloader(self):
         ds = load_dataset('squad', split='train')
         ds = ds.map(some_function)
         return [ds]

    def val_dataloader(self):
         ds = load_dataset('squad', split="validation")
         ds = ds.map(some_function)
         return [ds]
```
I don't know if it depends on `pytorch_lightning` or `datasets` but setting `ds.map(some_function, load_from_cache_file=False)` fixes the issue.

If this is not enough to replicate I will try and provide and MWE, I don't have time now so I thought I wuld open the issue first!
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