Testnet for bitcoin - are there multiple operating? I have been tinkering around on testnet with three portals:


Biteasy 
Block Explorer 
blockr


I observed that when I posted testnet coins using tpfaucet to a wallet created using testnetwallet, the transaction showed up in blockr and blockexplorer but not in biteasy. When I sent testnet coins using the same testnetwallet to a paper wallet address, the txn and balance showed up correctly in blockexplorer but not in biteasy or blockr.

I am a bit confused about what is happening here - I thought these are all services to look up the same testnet and hence I should be able to confirm same blocks, txns, addresses one each of these. Is that not the case? Are there private testnets operating on these portals? I can't see any information saying so anywhere.

Another observation: Blockexplorer is showing the transaction as confirmed with 74 confirmations and balance showing up correctly as confirmed balance in recipient account. But testnetwallet (sender account) is showing the txn amount under "unconfirmed" balance while the txn itself is showing up in history. Confirmed balance is unchanged at the moment in sender wallet. Blockr is not showing the transaction or the amount under the recipient address.

Day 2: testnetwallet.com now shows correct confirmed balance as the sender wallet. I can see the transaction, block and both receiver and sender accounts correctly using blocktrail.com and blockexplorer.com. Blockr and Biteasy still don't show anything - even when I search by block number. Will keep digging.

Day 3: today blockr is also showing the txn, block number and correct balances in both sender and receiver accounts. Until today, blockr wasn't showing any of these. Perhaps blockr service was slow/down? not sure. Biteasy is still not showing anything. I checked blockcypher also today and it's showing everything as well. I am going to use blockcypher's API to post a txn and check all five services to see which one is giving me results and by when. Will edit back with results.
There is no such thing as a private testnet, you can obviously create one, but then it won't be of much use to provide data regarding a private blockchain to the public.
The testing network (testnet3 presently) is the same for every user/developer.
BitEasy's block explorer for the testnet doesn't seem to be working. They don't have data even for dates a month prior to the date you asked this question.
As far as exploring the blockchain the data is concerned, you can do it yourself by accessing the block-chain on your machine after running the testnet bitcoind. The approach may be vary, but then the point being you can do it yourself if you know basic programming.