Is every copy of the blockchain the same? If I have an error within file should I be able to copy this file from a backup and reindex chainstate?
So I copied this file again from a backup of the blockchain. This is from a second node. But I would suspect the files are the same, right?

No. Blocks are downloaded out of order, but are written to disk in the order that they are downloaded. So the block index (which states where each block is located) will be different for every node because every node will likely have the blocks stored in a slightly different order.
Furthermore, if your node has received stale blocks, those stale blocks are also stored on disk and have an entry in the block index. Not all nodes will have the same stale blocks, and they may not be stored in the same order. Newly synced nodes will not have stale blocks from before they were synced, and often times stale blocks become stale due to propagation delays, so a node may not even receive a stale block to store.
You can't just copy individual block files from one node to another. You need to copy the entire blockchain and the block index. Otherwise you will probably corrupt the whole thing and need to redownload the blockchain.