Elo does not signify how strong of a player someone is.
Elo signifies how strong a player is in comparison to some community.
Assigning a numeric score to rank how strong someone is in chess would be very difficult to do. The way Elo works (and even the way it is designed) is simply to keep track of players in some group and make predictions about which player in that group is more likely to win against another player in that group. Having a score of 2100 in lichess means that the system has predicted you are more likely to win if you play against someone on lichess who has a ranking <2100, and more likely to lose if you play someone higher.
Having a ranking of 1800 on chesscom means that the system has predicted that you are more likely to win if you play against someone on chesscom with a ranking of <1800, and more likely to lose if you play someone higher.
Since presumably you play at the same level on both sites, that would imply that these numbers are more or less comparable. There are a lot of reasons that a player would have a different Elo rating in a different community
One community could simply be more skilled, or targeted at different types of players/
If the different communities have different "starting ratings" like you mentioned.
If the communities have a different size. In a smaller community, it's harder to get a very high Elo score (Imagine this taken to the extreme. If you track your Elo against one other player, you will get diminishing returns from beating them. Even if you are the best player in this "community", you will never hit Magnus Carlson level Elo scores)
It is possible for Elo ratings to differ between communities because of different standards of preventing cheating. But I would not expect that to be the case here, given that both sites have (Lichess, Chess.com) have written extensively about how they try to prevent cheating. If you feel like playing on one of these sites is unfair, reading through those articles can help you judge whether it's a fair place to play.
I know that there are many differences such as the starting rating of a new player on chesscom is 1200, but on lichess is 1500
That makes a huge difference. That means a score of 2100 on lichess is "1.4 times better than average" (which is an oversimplification of how Elo is really calculated and what it represents) whereas a score of 1800 of chesscom is "1.5 times better than average", which is a very minor difference.