Apple offers two AppleCare plans:
- AppleCare Protection Plan
Both of these are actually AppleCare products.
According to Apple:
AppleCare products for Apple Watch, for Mac, for iPod, for Apple TV,
and for Apple Display provide global repair coverage. Service will be
limited to the options available in the country or region where
service is requested. Service options, parts availability, and
response time vary by country or region.
All repairs will be completed using genuine Apple parts for repair
service. All repairs are performed by Apple-authorized technicians.
Therefore, only Apple Watch, Mac, iPod, Apple TV, and Apple Displays are covered by a global repair warranty (as you already state in your question). However, you're mistaken in assuming AppleCare+ is treated differently to the AppleCare Protection Plan, because they both fall under the category of AppleCare products, and the above quote applies to both.
In other words, while you can purchase AppleCare+ for an iPhone, this coverage will not be global. In your case, purchasing an iPhone in the US and also purchasing AppleCare+ will only cover you in the US. It will not cover you in India or anywhere outside the US.
In a nutshell, while AppleCare+ provides additional hardware and technical support from Apple (it even covers two incidents of accidental damage), it is not currently available in India, nor does it provide global coverage for iPhones.
However, Apple has reached a number of agreements with the government of India and is now investing a lot of time and money there. It is possible that at some future point AppleCare+ will be available in India. With this in mind it is always worth checking with Apple directly at the time of purchase.