The other question - and I know this must have been answered somewhere and I just couldn't find it - what determines transaction uniqueness? Say Alice buys a widget from Bob for 31.42 bc. Alice then decides she wants another widget, and places a new order - with the same keys for both buyer and seller - for another 31.42 bc. What makes these two transactions distinct? If a node sees one transaction for 31.42 from A to B, then sees a transaction for 31.42 from A to B, what tips it off that these are two distinct transactions rather than the same transaction detected twice?
A few things make those 31.42BTC transactions unique:+ The timestamps in them will be different.
+ The input transactions will be different (you can think of those as being different 'coins' going in to make the payment).
+ And if the input transactions don't add up to exactly 31.42 (and they probably won't), they'll have different output transactions for returning any change to Alice.
By the way: all that stuff is hashed together to give each transaction a unique 256-bit transaction ID (which you never see, but is used internally so Bitcoin can quickly figure out if it has already seen this transaction before).