The effect of a blurring tool is simply put, to decrease the amount of details in an image.
Gaussian blur
Gaussian blur is a widely used algorithm available in most visual editing software (video, games), It is also quite limited, but does a good job at smoothing noise and details in a picture.
Lens blur
Lens blur is like its name imply the one used to replicate lens blur.
Smartphones nowadays are trying to replicate the lens type blur (called bokeh), which is creating halos around distant, out of focus sources of light, by detecting edges and isolating subjects automatically. Of course, doing it by hand is more time consuming, but also more precise.
Low pass filter
Low pass filter is somehow comparable to gaussian blur. In its name, “pass” means only low details are accepted by the filter. The main difference is that the low pass filter tool comes with contrast, brightness and saturation slider embed.
The main difference between gaussian and a standard low pass filter is that the former is more conservative toward the edges and thus will be more aggressive overall.
If you do the following experiment: apply a gaussian and a low pass filter with the same radius parameter, and compare the effect of each separately, it will be clear that the gaussian filter is softer and respectful of the image while a simple low pass acts more like a curtain softening the whole image.
When to use: a good way to make your subject more eye-catching for the viewer is to blur out the surroundings. This can in fact be used to replicate the behavior of the depth of field when a lens, or even your eyes, are focusing on an object. Blurring when applied lightly (especially when the effect is softened with an opacity layer), can also be used as a way to reduce noise and other imperfections.