Network propagation is the number of nodes (computers running a bitcoin client) that have heard about your transaction.
Confirmations is how many blocks have included your transaction and how many blocks have linked onto that block. 1 confirmation means your transaction was included in a block, 2 confirmations means that another block linked onto that first one, and so on.
Until a transaction has been included in a block, it isn't considered to have really happened, regardless of how many nodes have heard about it.
Propagation needs to happen before a confirmation can occur, as a mining node needs to be aware of the transaction to include it in a block.
As of this moment, both of your transactions you linked are now showing as having 1 confirmation after being included in block 228337.
As for why it took so long to get a confirmation (468 minutes for the first one), no real idea. Might be something regarding some miners dislike for satshoidice. For example, the Eligius pool is configured to exclude any Satoshidice transactions from their blocks, as they view them as spam.