Index funds and ETFs

NTA guidance here indicates that average cost basis applies when purchasing or selling the same stock. Is the meaning of "same stock" based on the stock symbol? If so, an S&P 500 index fund (e.g., VFIAX) would not be the same stock as its corresponding ETF (e.g., VOO). It would also not be the "same stock" as another S&P 500 index fund (e.g., SWPPX). Is that right?

For US income tax, an ETF conversion (e.g., VFIAX to VOO) is not a taxable event and the cost basis of the mutual fund carries over to the ETF. Is it the same for Japan income tax?

If VFIAX shares are converted to VOO shares, will the resulting VOO shares be the "same stock" as other VOO shares purchased directly? Or would the converted shares still be the "same stock" as other VFIAX shares?