Shopify Functions API

So, I am having a little misunderstanding the the availability of the Functions API. Please, check if my statements are correct.

The Shopify Functions API is available for everybody through publicly listed apps.
The Shopify Functions API is available through Custom App only for Shopify Plus merchants.

So far, so good. Here I want to make sure I am understanding correctly:
Some functions of the Shopify Functions API are available only to Shopify Plus merchants.

Taking all the statements into account, I am understanding that:
Some of Shopify Functions API that are available through the publicly listed apps, are available only to Shopify Plus merchants. Would that statement be correct?

Also:
If I am making a custom app for a Plus client, all of the Shopify Functions API should be available in the case. Would that statement be correct?

Thank you for anyone taking the time to reply, I want to make sure I don't continue bashing my head trying to figure a solution for non-plus client.