UPDATED FOR ODOO 18.0:

Automation Rules with the On save trigger can run multiple times, depending on the model, because updates to one field might trigger updates to other fields.

One easy way to understand how this all works is to create a simple Automation Rule that runs on every update (does not have any trigger fields defined in When updating) and posts a message to the chatter with the old and new values.

Use code like this:

for record in records:
    if env.context.get('old_values'):
        old_vals = env.context['old_values'].get(record.id, {})
        new_vals = {field: record[field] for field in old_vals.keys()}
        record.message_post(body="OLD: %s - NEW: %s" % (old_vals, new_vals))

With ALL MODULES loaded, when we create a new Sales Order, choose a Customer (no other fields are given values) and SAVE we will see:

You can see that the Automation Rule runs twelve times as all updates are made to the record.