In our usage, a "cryptocurrency" means the native currency of a blockchain which is open and publicly accessible and derives its value from its status as a new type of money that anyone in the world can receive, send, and earn through participation in the blockchain. Bitcoin and Ether are examples. Permissioned blockchains, like the type MultiChain is generally used for, don't enable cryptocurrencies under this definition.
An "asset" is a token which is issued onto a blockchain, and generally represents something which does not derive its value directly from the chain. For example a bank might issue an asset onto a blockchain to represent some cash it is holding.