There's a difference between a laser being overspec and overdriving it.
Overspec laser is when laser is built according to specifications and it was set for a long lifetime, but it still outputs higher than expected.
Example, DPSS green lasers. Due to their complex internal constructions, the DPSS conversion process efficiency varies wildly. Sometimes only on average, 25% or so of IR output gets converted to green.
Which means, theoretically, if you have a 100mW IR pump diode, you'd get 25mW of green outside. Ofcourse realistically, efficiency does not scale linearily from low powers to high powers but you get the idea.
Now, overspec green laser happens when you have a 100mW pump diode but have 35 mW of green output instead of 25mW. That's when you manage to get the inner construction better than planned due to sheer luck, and gain extra output at no additional cost.
Direct diode lasers are very rarely overspec. Only time when that happens is when you get what is known as "freak diode", which outputs insane amounts of light compared to other diodes for same amount of input power.
That happens VERY rarily though, one in tens of thousands I'd say. We've seen very few 445nm freaks, I think RHD has one outputting 2.6 Watts or something, I know that member called Dustin (dlmb) once had a 405nm PHR that gave 300+something mW for only 180mA input current (normal is 100mW for 120mA), and I'm yet to hear about 650nm freaks.
DPSS greens are what's most likely overspec, because as I said, internal construction is complicated and to put it bluntly, a bit random, so you may hit lower powers than intended, as well as higher.
