When reading the documentation of BLE chip from a semiconductor manufacturer that there is a small real time kernel on board, not OS. This is probably just a stupid question, but what would be the difference between a full fledged RTOS vs a real time kernel in such a scenario.
There are a variety of opinions on that question. One, held by systems programmers and the like, is that an OS kernel is a minimal set of services to abstract the underlying computer hardware, making it easier to write an OS or even applications on the machine. OS kernels typically operate in their own space, separate from user space where the rest of the OS (or even applications) reside. There is also the concept of a microkernel (and nanokernel), which is intended specifically to serve higher level (e.g., user space) OS services--although different microkernels partition OS services differently in kernel vs. user space. Check Wikipedia as a start (although some of its related entries have some factual errors).
Sometimes the embedded computing community refers to a kernel as a minimal OS, expecting applications, not more OS functionality, to use the kernel.
This may seem like an insignificant distinction, but it does effect the design and implementation of the kernel.