IS= Image Stabilizer, on the canon lenses its a little switch on the side of the lens. It will also be written on the lens somewhere. When I shoot with my 75-300 with no IS I always increase my shutter speed to faster that 1/400 to avoid camera shake. Your 2nd shot was taken at 1/125 which is quite 'slow' for that focal length (zoom).
How how did you know it was taken a 1/125, or rather how do I find it out? Right, so yes my lens does have IS and it is on. I know how to change the shutter speed and have it compliment the ISO, f stop but I am not exactly certain how to use any of them as competently as I would like to be able too. A have a very basic understanding. Slower for moon shots, night shots. Faster for day shots.