No matter how innovative the personal health records (PHRs) or electronic health records (EHRs) become, given the highly fragmented and specialized US healthcare system they still need to exchange data in a secure way that preserves privacy and trust. That is the goal of health information exchange (HIE).
The key HIE technical challenges are easily understood. Parts of a patient's clinical data will often be stored in many EHRs. For a patient with four, five, or more chronic diseases (these drive half of all Medicare costs) research shows that this will typically exceed 10 EHR implementations from multiple vendors! A conscientious provider seeing such a patient would want a comprehensive view of all of this care in order to save time collecting information that already exists, avoid duplicating tests and procedures that have already been done, and prevent mistakes from lack of information.
Historically, there have been two attempted solutions: 1) store everything centrally and, in essence, create a community record, or 2) keep the data at the source but build central indexes to patients and their medical documents and provide some kind of translation service to bridge differences in the way clinical data is represented across EHRs. This is the so-called hybrid exchange.
More recently there is Fast Healthcare Interoperability Resources (FHIR), which is essentially based on the idea that healthcare information can be exchanged the same way that other information is shared on the Internet. If you've used Amazon to look for goods to purchase, you might have noticed that, up there in the URL, text appears when you click the search button that specifies what you want. Although it might be a bit cryptic, even a non-technical person can usually figure out most of what it says.
What's really going on here? You're at your computer (which, of course, these days might be a mobile device such as a smartphone), and the information you want is securely stored in, for example, Amazon's cloud. You specify what you want, and your browser creates a query and sends it to the cloud, where it might be routed to any one of thousands of Amazon servers that will interpret it, query a database, and return the information you requested. This ability to route requests to any server in the cloud that is available is another key technical property that lowers costs and is exploited in FHIR.
As with Direct, there is more to the story than I've described (technically inclined readers should read the FHIR Summary, which is also available as a two-page PDF). But this should suffice to give you the basic idea of what is increasingly termed "API-based HIE."