Would this be factor and not just one printing of one currency the issue of the inflation for all the countries?
You are correct.
Actually goods and services traded between countries can affect inflation in a country. If your country is exporting more products outside of the country to the rest of the world then it might help economic growth which can increase demand for its money.
The difference in value of different fiats can lead to higher prices of imported products which will also contribute to overall inflationary pressures in the country.