It depends on what type of file you are editing with Photoshop or Lightroom. Those applications handle raw files in a totally different way than they handle jpegs, pngs, or even tiffs.

The biggest difference between editing a jpeg using photoshop and editing it with most online editors is the degree of control over the adjustments. You will likely not only have finer gradations of control but wider extremes as well. Instead of a single hue and saturation control you can adjust the hue, saturation, and luminance independently for eight different color bands ranging from red, orange, yellow, and green, to aqua, blue purple, and magenta. You can use more sophisticated noise reduction with more user controlled variables. You can draw your own gamma curves instead of only adjusting for contrast and perhaps highlights and shadows.

But to get the full power and functionality of Photoshop, Lightroom (both use Adobe Camera Raw to process raw files, they just differ in the way the interface with ACR works), and other such applications you need to bring the raw file with all of the information collected by your camera's sensor.

When you save your files as jpegs most of how the photo will look is pretty well baked in. A high percentage of the raw data from the sensor is discarded and there is no way to recover it from the resulting jpeg file. At that point most of your editing options are to take away some of the information you have left. This is fundamentally different from editing a raw file in which you may discard some information from the interpretation of the data you see on your screen, but you also have the option to add information from the raw data that is not used in the initial depiction on your screen. You have as much flexibility with regard to color temperature, white balance, contrast, black point, white point, saturation, etc. as the sensor on your camera can record and which the application you are using can take advantage.