Are my crypto assets stored in the wallet or the App?

Please note that a "wallet" is a collection of ECDSA key pairs. A key pair consists of a "public key" and a "private key" which can be used to encrypt or sign bits of data. The public key, as the name suggests, is known to everyone and can be used to encrypt messages in such a way that the holder of the private key alone may decrypt them. The private key may also be used to sign messages in such a way that anyone holding the public key may verify that the message truly came from you. Every cryptocurrency address consists of such a key pair - the "address" you send people is the public-half and the private-half resides in your wallet data file.

The "blockchain" is a constantly growing database of transaction information which is sent out to all nodes in the cryptocurrency network. When you perform a transaction, that transaction is distributed to the network and assuming the transaction is valid, will be included in the next "block." This is where the coins themselves are stored. When you initiate a transaction, all previous transactions to or from that address are scanned and a balance is calculated. If your transaction exceeds this available balance, it will be rejected by the network and will not be included in a block.

Thus, your cryptocurrencies are neither stored in the wallet nor the App.