I am not saying an invalid TX, but a TX with a invalid output (the technical term may be unspendable output - an output in which it would be impossible for private keys to be associated with).
Once again an unspendable output isn't an output that is invalid, it is an output that is invalid. An invalid output means an invalid tx, and any block including it would be an invalid block and thus never part of the longest chain. For example a native multisig output which is greater than 3 of 3 is invalid. It will never be included in a block.
Unspendable =/= Invalid. Unspendable is just unspendable. It could be unspendable on purpose ("burning coins" or by accident (wallet software errors) but it is unspendable all the same.
gettxoutsetinfo
{
"height" : 305997,
"bestblock" : "00000000000000005c56379fc24b9b75c5c44c7afdb75f0c5b0801c56ec4f6bf",
"transactions" : 3305419,
"txouts" : 11452422,
"bytes_serialized" : 396365647,
"hash_serialized" : "10c14635b7ca03524099eb1bef0018480afddb67986b569fc9aa58bf1d16bb73",
"total_amount" : 12899789.79002854
}
To date 135.20997146 BTC have been destroyed.
(305997-210000)*25 + 210000*50 = 12899925.00000000 BTC
12899925.00000000 - 12899789.79002854 = 135.20997146
What my question is, how is a pool destroying coins by sending part of the block reward to an unspendable output different from broadcasting a TX with an unspendable output (with your own coins)
I have no idea what you are talking about. An unspendable output is an unspendable output no matter who creates it. Nobody said anything about a pool creating an unspendable output.
I was referring to this post about the pool claiming less then the 25 block reward
Miners (or mining pools) receive as their block reward, the sum of the block subsidy (currently 25 BTC) AND the total transaction fees paid by all transactions included in the block.
They do this by creating a special transaction that has no inputs, and assigns outputs that do not exceed this sum to any addresses (or scripts) that they like.
Notice, that I said they assign outputs that do not exceed this sum.
In other words, the protocol is perfectly happy to let a miner assign LESS than the reward that they are due in this transaction.
This has happened in the past accidentally. It is not likely to happen intentionally, but that doesn't mean it can't.