Basic Trope: A work, when translated, is more heavily edited for the new audience.
Straight: The Adventures Of Alice-chan is a popular manga in Japan. When it comes to the US, the company translating it removes a lot of the more questionable material such as sex, cursing, and drinking.
Even objects that imply violence, sexuality, and other unsavory facts of life are edited (read: say goodbye to kitchen knives, hammers, shirtless men, women in any clothes other than a full-length burqa, Super Soaker water guns, handcuffs when not used by police officers, etc)
The editing is not only done like the above, but also doesn't bother to change things to match the context. This makes Alice-chan's Running Gag of eating too much candy with sugar rush consequences seem disturbingly similar to a drug addiction, and Kenji's implied relationship with Satou turns Squick-inducing when the censored version makes them step-brothers.
Very minor changes are made such as a beer ad in the background becomes a soda ad, or blood is present, but is recolored or darkened so it doesn't look too gory.
There a an alternate version of the show for younger audiences, but the uncut version is available to.
Values Dissonance. Just because Japan finds it okay to show extreme violence and sex to children doesn't mean everyone does (especially America)
The creators want to appeal to more readers, so they tone down the content for their main demographic (but not their Periphery Demographic)
The Adventures Of Alice-chan is a popular manga with very young children in Japan. When it comes to the US, the company translating it adds things like drinking, sex, and drugs to try to play to an older audience.
Subverted: When it comes to the US, the translation company seems that they'll heavily censor it, but they don't.
Double Subverted: At least, they don't censor the first few issues. But when the Moral Guardians start complaining, they start censoring for real.
Revealing outfits are censored by use of magical censorship animals which bounce around ridiculously. The Hollywood Homely character doesn't get one because she's got nothing to reveal. (Happens in the "voluntarily censored" version of GUN×SWORD.)
Zig Zagged: It seems like they will censor it, but they don't at first. Then the Moral Guardians come a-knockin', but even then, they refuse to censor it.
No censorship is attempted and the translation company is upfront.
They just change the target audience.
They keep everything in, and it's a surprise it still got a "For Kids" rating.
Enforced: "You're telling me I have to follow these rules? Well, I guess you print the checks..".
Lampshaded: "Well, we've had to make a few changes to this popular manga..".
Invoked: A similar manga is summarily cancelled due to the influence of the Moral Guardians. So...
Defied: The translation company refuses to censor the manga, stating that they want to please their fanbase.
Discussed: "Alice-Chan, this is an intervention. Your need to collect innocuous bags of flour is not only bizarre but also out of control".
Conversed: "You really need to read the scanlation of Alice-Chan. The official release completely sidestepped her cocaine addiction".
Deconstructed: The censorship doesn't sit well with either audience. The intended audience finds it too childish, and the original audience finds the censorship pointless. As a result, they voice their displeasure in their buying options.