A "re-org" simply means switching to a different (though equally valid) version of the block chain. "Roll-back" is another word for "undo". I have never heard the term "re-roll".
In general, there are occasional splits (or "branches") in the block chain. This happens when two miners mine a block at about the same time. Each miner publishes their block and some miners adopt one block (block A) and other miners adopt the other block (block B).
The rule is that the "longest" chain is the "main" chain. In this case, both versions of the chain are the same length, but at some point, a miner will mine a block on one of the branches, making it the longest chain. At that point, all of the miners that were mining on the other branch must switch to the longest chain. This switch is called a "re-org".
Re-orgs happen occasionally, and are not a big deal if it only involves one or two blocks. In the Binance case, miners would create a branch of the block chain containing all of the transactions since the hacker's transaction, but excluding the hacker's transaction. If enough miners jumped on board, the new branch would become the longest chain. The re-org would be huge (100 or more blocks) and would be very disruptive.
Normally, a large re-org could never happen because it would cost miners a fortune to re-do that many blocks. However, Binance could pay for the re-org by giving miners the stolen 7000 BTC (70 BTC per block vs. 12.5 BTC per block).
re·org
/ˈrēˌôrɡ,rēˈôrɡ/
informal
noun
noun: reorg; plural noun: reorgs
1.
a reorganization.
verb
verb: reorg; 3rd person present: reorgs; gerund or present participle: reorging; past tense: reorged; past participle: reorged
1.
reorganize.
"in less than a year, we've been reorged three times"
They do not want to consider reorganizing, "
we decided NOT to pursue the re-org approach", no the 51% of the miners decide that. What they meant was roll-back or re-roll (otherwise their statements make no sense). How you going to ask for 51% of the hashing power LOL. 81% of it is in china.