There are 2 different types of files when it comes to these machines, or any CNC in general.
Raster = images made of pixels, a raster image will be engraved by scanning back and forth to generate the result, these are jpg, png, bmp files.
Vector = drawings with coordinates and paths, for T2Laser these are dxf and plt.
You can trace a raster to generate a vector, the real term for this process is vectorization. If you fill a vector it becomes a raster, unless you use a pseudo fill (hatching) in which case it is still a vector but appears like a raster.
Are you more or less confused now

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So if the design is for cutting you would want a vector, or if you want an outline like a line drawing a vector may be appropriate but for a picture, even black and white clip art like your design a raster is probably the correct format as you need it filled.