Solidity, is there gas-wise difference between transfer and call with 2300? - solidity

Question

I am trying the below code, elementary reentrancy example.
The current code works but transfer or send doesn't work. It reverts. What are the reasons?
Note: I chose setCaller to reenter to test the fact that updating the dirty state variable (already modified var in the same tx) takes less gas.
// SPDX-License-Identifier: Unlicensed
pragma solidity 0.8.7;
contract TestFund {
// success, if caller is itself.
address public caller;
constructor() payable {}
function getBalance() public view returns (uint) {
return address(this).balance;
}
function emptyFn(address dummy) public {}
function setCaller(address _caller) public {
caller = _caller;
}
function withdraw() external {
caller = msg.sender;
// require(payable(msg.sender).send(1 wei));
// payable(msg.sender).transfer(1 wei);
(bool success, bytes memory data) = payable(msg.sender).call{gas: 2300, value:1 wei}("");
require(success);
}
}
contract Attack {
function getBalance() public view returns (uint) {
return address(this).balance;
}
function attack(address target) external {
TestFund(target).withdraw();
}
receive() external payable {
if (getBalance() == 1 wei) {
TestFund(msg.sender).setCaller(msg.sender);
}
}
}