When a central bank buys government securities, is this exactly equivalent to printing money? When a country's central bank buys that same country's government securities, is this exactly equivalent to printing money?
There seems to be no agreement on this.
Federal Reserve FAQ:

Is the Federal Reserve printing money in order to buy Treasury securities?
No.

Carlo Cottarelli (2017, Ch. 7 &quot;Printing money&quot;):

central banks, by printing money, can help governments spend more than they collect in taxes. The difference (the deficit) can be bridged by borrowing not from private savers but from the central bank, primarily through the central bank’s purchase of government securities. Public debt increases, but if the securities are held by the central bank, any interest paid to it goes back to the government, which receives its profits even in countries where the government formally does not own the central bank. In other words, the portion of public debt held by the central bank is not to be regarded as real debt, at least not in the immediate future. This is essentially what has happened to varying degrees in many advanced countries, which have continued to run sizable deficits since 2008.

Who is correct? (Or, why the seeming disagreement?)
Concrete example: Say John is hired to mow the White House lawn for \$100. What then is the difference between the following two scenarios?

The US Treasury prints a \$100 note, then uses it to pay John.
The US Treasury issues a \$100 bond that the Fed buys, then uses the \$100 deposited in its account to pay John.
I don't know if you are aware that you are using the word "print" abusively but:


  The U.S. Treasury controls the printing of money in the United States. However, the Federal Reserve Bank has control of the money supply through its power to create credit with interest rates and reserve requirements.


Source : https://www.investopedia.com/ask/answers/082515/who-decides-when-print-money-us.asp

Thus both are correct. Clearly a CB does not increase the money supply by creating credits in order to buy governments securities. 

It does so with other goals in mind, such as forging economic cycles, maintaining financial stability, reconfiguring the debt market and/or stimulating money multipliers in the national economy. 

A CB (theoretically)(and indirectly) buys government securities in an inflation-neutral manner $\iff$ no money printed $\iff$ it uses the existing "stock of (scriptural) cash".


The difference between your two scenarios is the notion of debt. Strongly putting aside the fact that your ex-nihilo first scenario literally makes no sense without a credit underlier.