[Ethereum] Why are there two methods encoding arguments? “abi.encode” and “abi.encodePacked”

From the link in the question, the important part about nameReg.call("register", "MyName") is (bold mine):

to interface with contracts that do not adhere to the ABI, the function call is provided which takes an arbitrary number of arguments of any type. These arguments are padded to 32 bytes and concatenated.

See the note here:

Note: the ABI is an abstraction that is not part of the core Ethereum protocol. Anyone can define their own ABI for their contracts, and any callers of such contracts would have to comply with that ABI to get meaningful results. However, it is simpler for all developers to use Solidity, Serpent, and web3.js which all comply with the ABI above.

nameReg.call("register", "MyName") will not invoke register on a nameReg contract compiled by Solidity. The reason is that Solidity does not use "register" to lookup "functions" (it uses the first 4 bytes as the method id. For example EVM pseudocode that Solidity produces, see this). Here's code for a quick test:

contract NameReg {
    bytes32 public nn;
    bytes public calldata;

    function register(bytes32 name) {
      nn = name;    
    }

    function() {
        calldata = msg.data;
    }

    function doesNotCallRegister() {
        this.call("register", "MyName");
    }
 }

With anameReg contract compiled by Solidity, nameReg.call("register", "MyName") will invoke the fallback function where msg.data will be "register", "MyName" padded to 32 bytes and concatenated: 0x72656769737465720000000000000000000000000000000000000000000000004d794e616d650000000000000000000000000000000000000000000000000000.

The issue is that the RPC keccak is actually slightly different than the one used in Solidiy. To get hashes consistent with solidity, use the ethereumjs-abi library. For example:

var abi = require('ethereumjs-abi')
var BN = require('bn.js')

abi.soliditySHA3(
    ["uint"],
    [ new BN(1)]
).toString('hex')

> "b10e2d527612073b26eecdfd717e6a320cf44b4afac2b0732d9fcbe2b7fa0cf6"

This is the correct hash that you should use. Also, be sure to pass in the actual hex value to getStorageAt, i.e. by passing in the result of abi.soliditySHA3 without converting to a hex string.