CERN has a variety of techniques to access, store, and backup their data. I know from experience some experiments, or at least some parts of experiments, use layers and layers of abstraction, like scalla/xrootd which operates on clusters of servers directly or with nfs.

In addition to this, there's levels of processed data. For example, raw data is usually level 0, and basic processed data is level 1 Processed and calibrated data is usually level 2, etc... but experiments often have different definitions for each level. Reprocessing of any later can happen at any time, although level 1 reprocessing is usually an extremely intensive operation because it operates with the largest amount of data.

Level 0 data is usually heavily compressed when it's left on disk, because it's typically the largest amount of data, but also least touched.

Most scientists will use level 2 or level 1 data. This data will be on low latency clusters.

So, while CERN has petabytes of data, typically a fraction of that will be accessible.

In the past, level 0 data was often left to tape. While the raw data is still backed up to tape (I know this is the case for ATLAS), for many experiments with large amounts of data they might leave it on lower cost HDD in simple RAID arrays for redundancy and not worry about performance so much. The BaBar experiment has done this for their long term data analysis.

In addition to all of this, it's still occasionally easier to transfer large amounts of data via tape instead of the internet.