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The site you built will always be available in your SynthaSite account for editing and updating even if you download your site as a zipped file and host it elsewhere.
However, to put your changes live you would need to re-download your site and re-upload it to the servers of your hosting provider each time.
If you host your site with us (either using a free subdomain or a domain of your own) you can update it with a single click - so it is a lot easier to make changes.
This is an excellent question and a very important consideration when deciding where to host your site. Thank you for asking it.
I hope this information helps you to decide which option is right for you.