I am just speaking from the lense of my education, nothing more or less. In my study to be a History teacher intellectually and then a soldier and a LEO practically, tactics is the unit/individual methods used operationally to accomplish the strategy. Now outside of those worlds are the two words sometimes used interchangeably? Sure. But my co-workers call me Sheldon sometimes and my wife "fffing Mr. Spock"
A strategy is broad strokes. Think mindset and overall goals. So in your takedown technique example, it provides a new tool, thus tactic to achieve the overall strategy. It takes a huge leap for a tool to change tactics and thus inform strategy though. Think 18th century through 19th century warfare, the era that is referred to as the age of Napoleonic Tactics. They remained firmly entrenched (pun intended) until technology jumped clearly ahead in WWI with the mess that was trench warfare. Even the slaughters that were our Civil War and that of the Franco-Prussian war weren't quite enough to get war planners to change mindsets when it came to tactics. To continue the analogy if you had NO knowledge of takedowns at all, learning to execute them could influence tactics enough to create new strategies but if it is simply a new takedown, then all it does is give you a knew tactical tool to achieve existing strategies. Think this way, one element of the strategy of modern warfare is achieving air superiority. The fact that today aircraft can launch missiles beyond the horizon hasn't changed that BUT the introduction of effective combat aircraft added air superiority to the strategic playbook.
Like I said, while embarrassing. Juany = Sheldon, at least I own it lol.