It's a dream based world.
Paprika: Paprika is an identity used by scientist Chiba Atsuko in order to test out the machine through going in people's dreams and finding out the cause of their anxiety. Because of the nature of the process, Paprika is a secret identity, and with her being somewhat anonymous, her clients can feel at ease that nothing was going to come out.
Inception: The team of Cobb and Arthur started out by entering people's dreams to infiltrate and extract information from classified people. However, they were hired by Sato to plant an idea by infiltrating someone's dreams.
Dream manipulation has dire consequences.
Paprika: If dreams are tampered with in great amounts, the world between dream and reality would cross, allowing dreams to flow in reality.
Inception: The consequences of manipulating a dream can be seen in the presence of Mal, when Cobb left the spinning top, rendering Mal's subconscious and eventually her consciousness to not realize whether she is dreaming or in reality.
There is an alternative world.
Paprika: Somehow, Paprika and the people can cross into other people's dreams, as long as they're all using the machine. However, as a result of manipulation, people on machines can be rendered to endless sleep.
It's all about technology.
Paprika: The machine used in Paprika is small and is used by attaching it on the head. It's portable, and they don't have to share machines.
Inception: They only use one machine, and in order to access the same dream, they must all be attached to each other.
Paprika: While it doesn't necessarily affect the person's dreams Paprika's viewing, dreams can subsequently merge when there are multiple users of the machines.
Inception: Everyone gets affected by the thoughts, even if it was a simple thought.
It has a purpose.
Paprika: Used for science, to cure schizophrenia
Inception: Personal gain
Paprika: A person can do the job, but she also operates on a kind of "kick" as to not fall into deep sleep. Unlike Inception, the dreamer doesn't need a kick to wake up, rather they use the transition of sleep cycles.
Inception: While it only requires Cobb and Arthur, there is a lot of planning to be made in order to fully infiltrate and extract information while trying not to destroy the dream.