In my opinion, casual elements are whatever removes mechanics from a game for the sake of appealing to a wider audience, or just a lack of gameplay mechanics in general. For an example, I'll use XCOM and Command and Conquer.
In the original XCOM, you controlled a large set of soldiers, had a varying amount of turn units for each soldier per turn that averaged at around 50, a door of pure, unforgiving pain at the beginning of each mission, and a geoscape where the strategic battle played out in. In the new XCOM, you could only have up to six soldiers in a mission, you had up to two actions that could be taken per turn for each soldier, and a simplified version of the geoscape from the original. How much of each of these changes is making the game more casual? A max of six soldiers compared to the original twenty is a massive drop. But, whenever I play the original, I rarely used all twenty at once. I would almost always use about a third to a half of my space for tanks. So for the Skyranger I would have ten soldiers and a tank, while for the Avenger I would have twelve soldiers and two tanks. And even then I wouldn't use them all, , and the people I was using would be spread over a much wider area, operating my men in small squads. Meanwhile, in the new XCOM, you almost always use all your soldiers, and they are almost always working together, only occasionally being split up on the lower difficulties. So instead of removing complexity, you are mostly just changing the scale of the battle, while making the individual soldiers more valuable.
Next you had the turn units. On one hand, with only two actions, there is a lot less that can be done. You either move, move and do an action, or do an action. But really, what are you going to do with 60 TUs? Not really much will be different, but now you have to spend a minute crunching numbers to check if you will have exactly enough to run over, throw a grenade, and try to get to cover. So there you are mainly sacrificing a small amount of extra mechanics for a much more streamlined experience.
Then you have your delivery into battle. In the original, you dedicated at least one third of your troops to getting shot as they stormed down the platform, giving the rest of your squad time to get to the area surrounding the skyranger, making them a perfect target for grenades and blaster bombs. In the new XCOM, you start the mission on the ground already, most of the time with no ememies in site. However, instead of being a case of purposely removed mechanics, this is a symptom of a lower scale of combat and a change in TU functionality, since losing just one or two soldiers straight off at the beginning would be a heavy loss.
Finally, you have the geoscape. From what I understand of the developers reasoning behind their simplification of it, most people only built extra bases for fighter coverage, so replacing extra base functionality with satellites was an acceptable thing to do. This is the only major change that can truly be called casualition, because there are entire mechanics that have been removed to make it easier for new people to play. In the original, you had to make the choice between placing all your eggs in one well defended basket, or spending the extra money to diversify your bases, allowing a total loss of your main base to be recoverable, at the cost of more spent money and extra management. The loss of this functionality basically renders the geoscape to an issue of money, with finding the best balance between satellites, panic, and fighters.
So, overall, most of what was done was changing the core mechanics while still keeping most of the complexity, with a few exceptions. However, when you get to Command and Conquer Four, what happened was mostly a loss of mechanics. Having not actually played the game, I can't comment on the specifics. But in early C&C games, you had a heavy emphasis on base building. In the few MP games I played with my friends, along with in single player, you would have multiple bases. Some would be large, sprawling bases that can do everything, some would be secondary bases, some would be just resource outposts, and some would be for being a dick to the other player by use of artillery and bomber emplacements. However, C&C4 got rid of this, replacing it with some kind of Crawler shit that did all your resource management for you. This gets rid of an entire field of mechanics, replacing it with something completely different, all in the name of making the game accessibly to a completely different audience.
So, TL;DR, a casual game has a loss or lack of complexity with nothing to make up for it. There are no complex maneuvers that can be discovered or practiced that allow for a longer amount of gameplay, no stories that can be told, and no deep insight into the human condition that is gained.