Constants are variables in a experiment that stays the same for example your testing what fertilizer helps grow a sunflower better and you give the plant 1 cup of water a day. The sunflower, and the one cup of water are constants because you don't change them. Now a control group is what it is being compared too, so if you give a plant no fertilizer to grow and you will be comparing the one's without fertilizer too plants with fertilizer which is your control group. (the plant with no fertilizer)
Therefore the different between constants and a control group? Is that "control groups get compared to other test subjects, and constants dont get compared at all." (Because they stay the same)
Hope this helps!
