If I create a private blockchain using Geth and mine ether using mine.start() in my account, the ether that is mined, is it real or just test ether ?
These are just test ethers. They have no real value.
On a private chain, that is just "private test ether" with no value to anybody else. If your node is not publicly accessible (private), only you have access to it, therefore it is your "personal" testether.
Have a look into the different networks here: http://ethdocs.org/en/latest/network/
Ether on a certain blockchain network is only valid on this blockchain. So it is worth nothing, unless somebody participates on the blockchain and wants to buy ether, which is unlikely.
You can not transfer ether between different blockchains, because your mined ether on your private blockchain is generated by creating blocks. After a successful creation of a block, you get a reward for creating it. But on the other network you did not create this block and therefore you do not own the reward.
You are able to use the same wallet on different blockchains, because it is just a valid private key. But the balance will be different, as it is derived out of the transactions that happened before on the network. See this answer for more information on this topic.
Making a private blockchain is like building a bank in your backyard and printing your own money.
The currency doesn't have any value, you have total control over it and you can print any amount you want, but no one will trade it for real money.