To get an answer to this question we can look at the source code for Parity-Ethereum and the documentation for the trace module.

There are two distinct definitions in the source:

Action

/// Action
#[derive(Debug)]
pub enum Action {
    /// Call
    Call(Call),
    /// Create
    Create(Create),
    /// Suicide
    Suicide(Suicide),
    /// Reward
    Reward(Reward),
}

CallType

/// Call type.
#[derive(Debug, Serialize)]
#[serde(rename_all = "lowercase")]
pub enum CallType {
    /// None
    None,
    /// Call
    Call,
    /// Call code
    CallCode,
    /// Delegate call
    DelegateCall,
    /// Static call
    StaticCall,
}

So here we can see that every trace has an Action (represented by type in the JSON), and if the Action is a Call, then it can have a CallType (represented by calltype).

To get an answer to this question we can look at the source code for Parity-Ethereum and the documentation for the trace module.

There are two distinct definitions in the source:

Action

/// Action
#[derive(Debug)]
pub enum Action {
    /// Call
    Call(Call),
    /// Create
    Create(Create),
    /// Suicide
    Suicide(Suicide),
    /// Reward
    Reward(Reward),
}

CallType

/// Call type.
#[derive(Debug, Serialize)]
#[serde(rename_all = "lowercase")]
pub enum CallType {
    /// None
    None,
    /// Call
    Call,
    /// Call code
    CallCode,
    /// Delegate call
    DelegateCall,
    /// Static call
    StaticCall,
}

So here we can see that every trace has an Action (represented by type in the JSON), and if the Action is a Call, then it can have a CallType (represented by calltype).

These are all generally represented by the Ethereum OpCodes:

Calls

0xf1    CALL    Message-call into an account    -   Complicated
0xf2    CALLCODE    Message-call into this account with alternative account's code  -   Complicated
0xf4    DELEGATECALL    Message-call into this account with an alternative account's code, but persisting into this account with an alternative account's code  -   Complicated
0xfa    STATICCALL  Similar to CALL, but does not modify state  -   40

Other

0xf0    CREATE  Create a new account with associated code   -   32000
0xff    SELFDESTRUCT    Halt execution and register account for later deletion  -   5000*

Not very sure about Reward, but here suggests it is for uncle and mining rewards.