The Sims 3
Bella Bachelor and Mortimer Goth both appear as children, both seven days away from becoming teens. They both live in Sunset Valley, although in different households, as Bella lives with the Bachelor family and Mortimer with the Goth family. They are best friends, and Mortimer is also friends with Bella's older brother Michael Bachelor. As the two are playable Sims, it is possible (although optional) for the player to develop a romantic relationship between them, although the same applies to any unrelated Sims with a small enough age difference.
The Sims Bustin' Out
Bella and Mortimer are married and live together in Goth Mansion. The two appear as adults. Cassandra is not living with them, and whether she wasn't born yet or has already moved out is not specified.
Bella and Mortimer are both adults and live together in 5 Sim Lane (or 5 Sim Avenue in the console version). They have one daughter, Cassandra Goth, who is a child and lives with them. In the console version, they have a relationship of +90, with the maximum being 100.
The Sims 2
By the time the events of The Sims 2 take place, Bella and Mortimer have had a second child called Alexander. Bella also got abducted by aliens, and is currently missing. When exploring Mortimer's memories, many of them involve Bella, indicating she hasn't been missing for too long. In the PSP version of The Sims 2, Bella's secrets state that she married Mortimer for his money.
The Sims 4
In the alternate reality, Bella and Mortimer are married, similarly to the main reality. They have a more notable age difference, as Bella is still a young adult while Mortimer is an adult at the beginning of the game. They live in the Ophelia Villa house in Willow Creek with their teen daughter Cassandra and child son Alexander.
Cassandra is the first child and only daughter of Bella and Mortimer Goth. She appears as a child in The Sims 1, adult in The Sims 2 and teen in The Sims 4, and lives with the Goth family. In The Sims 2, she is engaged to Don Lothario.
Alexander is the second child and only son of Bella and Mortimer. He appears as a child in The Sims 2 and The Sims 4, and lives with the Goth family. He also appears in the DS version of The Sims 3, where he is a young adult and married to Cecilia Goth.
As The Sims gameplay generally focuses on custom characters, Mortimer and Bella are usually only seen as a background couple, if even that. The pairing between the two is mostly acknowledged by people focusing on the pre-made Sims, often to discover secrets behind them. The couple also has some fanfiction about them, and on AO3, it is the second most popular ship in The Sims fandom, although only featured in approximately 5% of all fanworks in the fandom. The name "BellaMort" was used for the two on at least one Sims forum, where the name was noted to be the same as the ship between Bellatrix and Voldemort from Harry Potter (the latter typically has a lowercase m).