A task sequence is a series of actions (known as tasks) that can be assigned to a task executor (such as an Operator or Transporter). You can also read more about task sequences in the user manual if you search "Create Task Sequence" in FlexSim.
A sub-flow (also known as a sub process flow) is a separate process flow that begins running when it is triggered by another activity or event in a different process flow. You can also read more about sub-flow if you search "Sub Process Flows" in the user manual.
You can start a task sequence without Start-Finish activities. Usually you will start with a Source. Start-Finish activities are usually used when creating sub-flows.
I've attached below an image of a simple internal sub flow.
creating-internal-sub-flows.png
For more information I would highly recommend searching "Task Sequence" in the FlexSim User Manual. If you still have more questions we are happy to answer them.