Hi there,
Thanks for the question! I can certainly speak to Keyword Explorer's numbers and how we arrived there. We use a number of sources for our volume data, including Keyword Planner, but oftentimes you will see large discrepancies because our data goes through a disambiguation process. As you noticed, Google Keyword Planner currently bundles similar keywords into one overall volume metric. Most people want specific data rather than a grouped number, so we strive to separate out the individual keyword volumes. You can read more about that here: https://moz.com/blog/google-keyword-unplanner-clickstream-data-to-the-rescue
The trouble is that often times you will have one keyword that is responsible for upwards of 95% of the traffic. So, when the data is separated out, it makes the less-trafficked keywords look suspiciously low when in fact their traffic volume is more accurate in our tool.
We have a few additional articles that discuss our volume data compared to Keyword Planner:
https://moz.com/blog/google-keyword-planner-dirty-secrets
https://moz.com/blog/moz-keyword-explorer-vs-google-keyword
I hope that helps clarify things!