In SQL Server, a "database" is synonymous with "schema": a collection of objects like tables, views, etc. In Oracle, "database" is synonymous with "server" or "instance" - the set of running processes and the data files they support (stand-alone, CDB, or PDB). In Oracle, a "user" that owns objects (tables, etc.) is synonymous with "schema", so an Oracle "user" is conceptually the same as a SQL Server "database". When connecting to Oracle whether using OCI, ODBC, or JDBC clients, you must always choose an instance (using SID or Service Name) and a user/schema.
To answer your question on determining the current schema in Oracle: when connected to an Oracle database instance, the current_schema session parameter determines which schema oracle will direct your queries to by default if you do not fully qualify your object names. It can be set using the following command:
alter session set current_schema=[username];
Existing session parameter values can be found by querying the sys_context function:
select sys_context( 'userenv', 'current_schema' ) from dual;
select sys_context( 'userenv', 'session_user' ) from dual;
See here for more on sys_context: https://docs.oracle.com/en/database/oracle/oracle-database/19/sqlrf/SYS_CONTEXT.html#GUID-B9934A5D-D97B-4E51-B01B-80C76A5BD086
For more on how Oracle schemas and SQL Server databases compare, see these previous posts on the subject from dba.stackexchange.com and stackoverflow.com: