It is strange but I noticed cast iron plates seem heavier than rubber coated plates. Weight plates in my gym are rubber coated. I have bought some weights for home workout. But the same weight feels different. It seems like cast iron plates are more pulled by gravity. It's not only me; my cousin also confirmed the same. What would be the reason for it?
1. The weights are actually less
A gym I used to go to had two different kinds of plates: rubber coated and cast iron. Out of curiosity, some patrons of the gym brought a scale and compared the weights of all the 45 lb. plates. The cast iron plates were all about 45 lb. with small variation of ±2 lbs. So some were 43, 44, 46, and 47 but all around the mark. The rubber coated plates on the other hand were all just really off. Not one was above 42 lbs. A couple were as low as 38 lbs. I can't say if this is a problem for all rubber coated plates, but... rubber coated plates tend to be cheap, and cheap equipment is cheap for a reason.
2. It's in your mind
The current gym I go to has three kinds of plates: cast iron, calibrated iron, and calibrated bumper. Calibrated plates have a very small margin of error, hence they are used in competition settings. The cast iron are the same type as in the other gym. So their weight should be relatively the same. However, when I use the calibrated plates they just... feel heavier. Something about it makes my brain think "These should be harder" so it makes them harder. Particularly the bumper plates because because they're so wide that they seem heavier.
Interestingly, there is actually a tactic where you purposely don't use big plates so that you don't get as nervous using them. For example, if you're attempting your first two-plate bench press but you get nervous when unracking, it may help to remove one plate and use smaller plates to add up to the same weight. It may suddenly seem less intimidating, so you manage to push the weight. Then the next time you attempt two plates you will have an easier time because you've already pushed it.
3. Increased bar whip
This really is only an issue with heavier weight. Some rubber bumper plates are just really wide. This pushes the weight further down the sides of the bar which increases leverage on it. This causes more "bar whip" or bending of the bar. In certain circumstances, this might actually make the lift harder. For instances, at the bottom of a squat, if you drop really hard, the weight will continue to fall as the bar bends, which of course bears down on your back. Then it will typically bounce back up a little which could be used to your advantage, but most people don't wait a second before going back up. So if you push up while the weight is still going down it will feel a little heavier.
Overall though, weight is weight. So if your home gym's plates are lighter than advertised, you could mark the true weight on them and adjust with smaller plates to make up the difference. You could also just focus on progression. As long as you use the same equipment, you'll get the same results. Just keep in mind that when you move to better equipment that you'll probably have to lighten the load a bit.
Weight plates marked as 45 lb will typically weigh between 43-47 lb, about +-5% (maybe 10% on the high end), unless they're calibrated plates (in which case they should be with 10 grams). My old gym used to have the actual weight of plates marked on them with chalk.
So, it could be that you have one set of 'light' plates and one set of 'heavy' plates. You wouldn't know unless you weigh them.
My guess is there's a difference in the way you carry them. The rubber coated plates we had had handles molded in that made them convenient to carry. The iron plates you just have to pinch grip. That convenience can make them feel lighter.