A small overview:

• PulseChain (www.pulsechain.com) is the blockchain, the ecosystem, the network, the environment. 
• Pulse (PLS- proposed ticker symbol) is the native main coin of the PulseChain system.

It’s easy to be imprecise and use Pulse when you really mean PulseChain, and vice versa; in the same way people use Ethereum to indicate Ether ETH.