Oracle file permissions expdp vs dbms_datapump
I assume that the database runs on a Linux OS. 
I assume that you connect with a tool like sqldeveloper to the database using a tns-connection string (maybe from a machine different)
I assume that you start expdp from the database server using not a tns-connection string but set ORACLE_SID and create a local connection.


Then, yes, it is possible that such strange things happen.

In one of your comments you wrote "both run as a job in the database". That is not the correct terminology. Both are sessions in the database And both sessions have a Linux process that corresponds to the session: the so called shadow processes. There are more complex configuration but I assume this one.

So what is the difference between your two sessiosn? The way you connect to the database and the shadow processes are created.

In the case of the sqldeveloper that uses a tns-connectstring the tool contacts the listener and the listener-process runs the oracle binary to create a process (the shadow process). If you  run the expdp tool directly on the Server using a local connection then the expdp tool runs the Oracle binary to create a process. 



There are other situations were you can have such a result, e.g. with a RAC-Database. The database Directory Points on both nodes to a loacal Directory with different permissions.

But without more detailed Information it makes not sense to investigate this further.

Use a tns-connection in both Situation so that your shadow process is created in the same way.