Here's the full answer. Tools like my tool (Keysearch), KWFinder and a few others get their data directly from Google in realtime. If you notice a difference between KWFinders data and Google's data there are 2 reasons.
1 - KWFinder "cleans" close variants. Meaning they use this method here
http://searchengineland.com/get-old-google-keyword-planner-volume-254736 to clean keywords Google has deemed a close variant. Sometimes this is accurate sometimes not so much.
2 - They cache their data for a short time (I believe 30 days). Google updates their search volumes about every 30 days. Sometimes that 30 day span is different than KWFinders caching so there maybe a few days where their stats differ.
SEMrush also gets their keyword data from Google but doesn't do it in realtime. More popular keywords data get updated more often and less popular keywords data can be a few months old. Why do they do this? Because it allows them to use their own database rather then worrying about issues of scraping Google and realtime API limits.
So some say "Wait! SEMrush keyword data can sometimes be months old?" Yes. And it barely matters. Let's say SEMrush says a keyword has a volume of 1600 because it scraped it 3 months ago and haven't updated it yet. Now you go to Keyword Planner and see it's now 3600. That's a pretty big difference right? Well what does it matter? If you are doing keyword research today, pick a keyword, start building a page or site around it, in 3 months that volume is gonna change anyway again. So keyword volume is all about a basic "idea" of volume. It's always changing. Maybe next month it's 1600 again after you've already built the site. So caring about it matching Google at this very moment is kind of pointless as long as it was accurate at some point it should give you an overall idea.
Ahrefs and MOZ use clickstream data for keyword volumes. Clickstream data is search data collected by 3rd party services such as jumpshot from users browsing history. They then have an algorithm that compares that to google data they scraped a while back and have models predicting what the search volume should be. So their data will usually not match Google at all but in reality might be more accurate. Who the hell knows! All we know is Google's search volume data has always been questionable. My advice is don't get hung up on "Whats the exact correct search volume". Just get a basic idea. Is the keyword bringing in some traffic? Is it easy to rank? Go for it!