Is the 'Burp' mentioned in this, the 'Burp Suite' that can be downloaded here? https://portswigger.net/burp/communitydownload

Am new to this kinda stuff but would love to play with it. Always love reading up on responsible disclosures.

Yup, 'Burp' refers to the free version of 'Burp Suite'. I don't use Burp Suite anymore though. Some months ago I started using mitmproxy (https://github.com/mitmproxy/mitmproxy) due to it's Python scripting API. I have never looked back since then.