What does malleable mean in "transaction malleability"? Does malleable mean modifiable?

If you can malleate a transaction you can modify some of its parts leaving the transaction as still valid (the signatures are not broken).

If you can malleate the transaction outputs you can modify the outputs.

If you can malleate the order of inputs you can modify the order of inputs.

But the bitcoin.stackexchange.com "transaction-malleability" tag says: 


  A property of Bitcoin transactions that allows them to be replicated
  with another transaction id before they are included in a block.


This confuses me. Does transaction have an ID at all, and if it does ID seems totally irrelevant?
Malleability is ability to change the binary contents of transaction (that also includes its TXID) without invalidating it, by someone else after broadcast and before the confirmation in block.