Static stretching is things like sitting on the floor with one leg straight, the other pulled in to your groin in a half butterfly stretch and putting your head to the front knee. Or sitting with your legs apart and slowly holding your head as near to each knee (and then the centre) as you can. Holding it for a 5-8 seconds in each position.
Instead of head to knee, I like stomach to upper thigh. I try to make my body as long as possible. Head to knee curves the spine and people end up stretching their neck to reach that knee instead of stretching their legs.
The distinction is made clear in Dr Tom Kurz's book Stretching Scientifically, where he also goes on to show (with lots of references to scientific research) that static stretching is useless unless your sport demands it (maybe gymnastics) and has a detrimental effect (as it anaesthetises your muscles causing them to not respond optimally for a period afterwards and risking damage because they are anaesthetised).
I have his book, but never put his theories to use because I could already do the splits, which I got and maintain using a combination of static and dynamic stretching.
When we're warming ourselves up, I purely do a dynamic and static active warm-up. On non-Taekwondo days I'll do isometric stretches to increase my maximum flexibility, the dynamic warm-up helps me make the most use of my maximum flexibility.
Using Tom Kurz's methods, have you been able to achieve the splits?