Okay, you have to start at the beginning to get the terminology.
First, there's "emitter lumens" or "LED lumens", which is what the emitter is theoretically capable of producing at the drive current used, and sometimes it might be also what it actually does produce in the light at the emitter ONLY.
Then, there are losses in the reflector system or the optics, and also in the lens and possibly from reflections, so how many lumens actually comes OUT THE FRONT of the light is where we get this "OTF" term. It is typically somewhere around 15% less than the emitter lumens, although it can be more or less than that, depending on how good of a job was done with the light and its parts.
The ANSI lumens are OTF lumens which are measured at 30-120 seconds after the light is turned on.
The emitter starts to heat up almost immediately after turn-on, and the output starts to sag. Depending on how good the thermal management design of the light is, it might only sag a few lumens, or it might sag a hundred lumens or more. So, the ANSI lumens figure gives you some insight into how well the light can sustain its OTF output for some short time after turn-on, at least.
A light with good thermal management will sustain a very high percentage of its OTF lumens at turn-on, for most of the run-time of the battery that's in it. As lumen outputs get very high, and the lights are not very big, then it gets harder to manage this thermal load, and the light may start to show rapid decline of lumen output shortly after turn-on, and the light gets excessively hot. This shows that the light was designed with too much output for it to manage its thermal load properly, and the typical manufacturer's method to deal with this is a "step-down" of the output automatically, to a level that it can much more likely sustain, such as half-power.
There are games played by manufacturers with this step-down function, and they typically try to time the step-down at a time just after the time specification for the ANSI measurement, so that they can claim maximum OTF lumens at turn-on, and then automatically step-down the output after 2 minutes or so, and then they can advertise an "ANSI lumens" rating that is actually much higher than the light can sustain, and will pretty much only be useful at that level in a short burst function. They will tell you it is a "750 lumen light", when it actually is a 750 lumen light for 2 minutes, and then it's a 480 lumen light after that.
This is extremely common to the point that it is almost standard procedure on Chinese made lights, so you have to watch out what you are buying. They do it because it is much cheaper to put in a timer to step-down the light after a couple of minutes, than it is to design a light with proper thermal management characteristics. Basically, you can have the worst thermal design in the world, and still get a high "ANSI Lumens" rating with a step-down after 2 minutes. And that's exactly why they do what they do. The Chinese lights almost all essentially side-step the ANSI ratings with this scheme, and the ANSI Lumens spec is basically meaningless in Chinese lights because of this.
If you know that's what it's going to do, and you are okay with it doing that, then there's no problem.
