Consistency in ACID and CAP theorem, are they the same? From my understanding, the consistency in ACID is ensuring the data integrity.

However, the consistency in CAP means the data can appear quickly in distributed system.

Does that mean: they are not the same concept?
They are not really the same, because of the scope of the data
ACID

Atomicity
Consistency : All Applied Data Changes Provide Consistent View of Data For All DB Connections
Isolation
Durability

CAP

Consistency (All Nodes Have Same Data via Eventual Consistency)
Availability
Partition-Tolerance : system continues to operate despite arbitrary message loss or failure of part of the system

SYNOPSIS

ACID addresses an individual node's data consistency
CAP addresses cluster-wide data consistency