They are not really the same, because of the scope of the data
Both C's stand for consistency, but the notion of consistency in CAP means that "all nodes see the same data at the same time" and the notion of consistency in ACID means that "any transaction the database performs will take it from one consistent state to another". (From Wikipedia.)
CAP theorem is actually a bit misleading. The fact you can have a CA design is nonsense because when a partition occurs you necessarily have a problem regarding consistency (data synchronization issue for example) or availability (latency). That's why there is a more accurate theorem stating that :
During a partition in a distributed system, you must chose between consistency and availability.
Still in practice it is not that simple. You should note that the choice between consistency and availability isn't binary. You can even have some degree of both. For example regarding ACID, you can have atomic and durable transactions with NoSQL, but forfeit a degree of isolation and consistency for better availability. Availability can then be assimilated to latency because your response time will depend on several factors (is the nearest server available ?).
So, to answer your question, this is usually marketing bullshit. You need to actually scratch the surface to see what the solution is exactly gaining and forfeiting.
If you want deeper explanations you can look here, here or here.
