Moving a table to a different tablespace in Oracle using Online Redefinition Vs Alter table move tablespace
Those two methods are very different.

Alter table mytable move mytablespace


will move all the data blocks into the new tablespace. while it doing so, the table will be locked for DML.

DBMS_REDEFINITION will allow you to create a new table on the desired tablespace and sync the data between them ONLINE. when the sync ends the tables names will be switched.
you will have to be careful with DBMS_REDEFINITION as you have to create the new table youself including indexes, constraints, partition, privs, etc.