No. "cutting" and "bulking" are achieved through energy balance, i.e eating less or more food than needed to support the work you do.
The only reason to ever lift weights that feel light is if they are part of a rehab/prehab/mobility program.
All of your work in the gym should be done with heavy weights. Heavy in the sense that your sets feel challenging at whatever rep range you are using. Different rep ranges tax your heart, lungs, muscles and nerves in different ways. Most serious lifters work primarily in the low (3-5 reps) or moderate (8-10 reps) ranges, and commonly in both. Many people will also do some work in the high (12+ reps) range either as part of a warm up or as a "burn out" set at the end of a routine.
Heavy weights give your body a reason to preserve muscle when in a caloric deficit (cutting) or build it when in a caloric surplus (bulking).
Maybe not the same, but I think most serious trainers would rather see you cut back a set or rep here and there than cut the weight of those reps to "light." But there is good cause for ocassional days of 15-20 reps.
The reasons for using a specific program and rep scheme can vary quite a bit, and you should always be making progress (i.e the weight on the bar is going up). But generally, yes, manipulation of diet is the key to gaining and losing weight.
There may be some benefit to light weight 'circuits' during a fat loss phase, but as a supplement to a typical heavy lifting routine not a replacement.
It depends on what you prefer. My routine changes quite a bit when I move from pure strength or mass building to cutting. I drop volume (in light of caloric deficit), drop my rest intervals like crazy (only 0-45 sec), and move from upper/lower splits to total body training. It is mostly diet, but you do need to find some seriously metabolically challenging workouts in the cut if you want to expedite the process.