What's the difference between 1151 CPU and a 1151 (300 Series) CPU ?

Microsoft Community is a collection of forums for peer-to-peer support of Microsoft products.  Your question relates to Intel products and is far outside the scope of these forums.

That said, a little searching with your favorite search engine would reveal that "300 series" refers to the chipset used on a motherboard.  The chipset is the circuitry that controls the communication between the CPU, the memory (RAM), and various peripheral devices.  See, e.g., https://www.howtogeek.com/287206/what-is-a-chipset-and-why-should-i-care/ and https://www.tomshardware.com/news/chipset-definition,37655.html

The physical interface between a CPU and the motherboard is the "socket," and different CPUs require different sockets.

The LGA 1151 is a socket "which comes in two distinct versions: the first revision which supports both Intel's Skylake^[2]^ and Kaby Lake CPUs, and the second revision which supports Coffee Lake CPUs exclusively" (Wikipedia). 

As Intel explains,

 9th and 8th Generation Intel® Core™ Desktop Processors use an LGA1151 socket. However, they require motherboards based on Intel® 300 Series Chipset. Some Intel® 300 Series Chipset based motherboards may need a BIOS update to support 9th Generation Intel® Core™ Desktop Processors. Please check with your motherboard manufacturer for details.

These processors aren't backward compatible with motherboards based on Intel® 200 Series Chipset and Intel® 100 Series Chipset.

Similarly, 7th Generation Intel® Core™ Processors and 6th Generation Intel® Core™ Processors aren't compatible with the Intel® 300 Series Chipset motherboards.

The Desktop Intel® Core™ processors 6th and 7th Generation support both DDR3 and DDR4 memory.  The Desktop 9th and 8th Generation Intel®  Core™ processors supports only DDR4 memory.

Learn about Intel® Core™ Generations.

In other words, the difference between an "1151 motherboard" (not an "1151 CPU") and an "1151 (300 series) motherboard" is the type of CPU that can be used. 

The "300 series" can use 8th and 9th generation Intel CPUs.

The earlier version can use 6th and 7th generation Intel CPUs.

You can tell the generation of an Intel CPU by the number that appears after i3, i5, i7, or i9.  For example, an Intel Core i7-9700 is a 9th generation CPU and would require an 1151 series 300 motherboard.