I can change shipping method and default country from back-end settings as:
Store -> Configuration -> General -> General.
How to set up default shipping method and payment method for two different countries?
Much appreciated your help.
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In the configuration at the left top there's a dropdown next to "Store View", in this dropdown you'll find the websites and stores you have available in your installation.
Pick the website for which you want to enable or disable functionality, then go to the shipping methods and enable or disable them accordingly.
If want to achieve two different prices in two different countries. You can create two different stores for different countries in magento2 and set the Price and shipping charges according to their countries.
You need go and create stores for different countries
stores -> settings -> All stores -> create store.
stores -> settings -> configuration -> General -> General -> Country options -> change (default country) to respected country to want to add shipping
and to set shipping method
stores -> settings -> configuration -> sales -> shipping methods.