Your technique is the method (or what) and your style is how. Technique suggests tools and materials. Style has to do with flair, your voice (which we hope is unique) and often alludes to time periods, geographic region, movements or the manner in which your technique is employed.
Painting technique: with a roller Painting style: sloppy or neat Cutting technique: julienne Cutting style: French & precise
More seriously, techniques include terms such as monoprint, watercolor, acrylic, oils, drybrush, subtractive, reductive, etc. Styles could include terms like realism, abstraction, Deco, fauvism, impressionism, surrealism, minimalism, Prairie (architecture), etc. There are as many techniques as styles and they should not be confused.
These ideas extend to all visual/design disciplines. For example, fashion is the (contemporary) what (shirt) and style is the how (collar up, over-sized, deconstructed, etc).
The style requires analysis while the technique requires acknowledgment. For example, the technique is embroidery and the style is Nahuatl.
Figuring your technique is easy. Developing a style can take considerable time and often changes just as soon as you can define it.
technique: prismacolor on index (which in this case is also the media used style: skewed, quirky representation