Which of these two MYSQL queries is better (and what is the default join type)? My SQL:

select count('1')
 from plays,
      promotion, 
      partner 
where 
  partner.id = 1
  and promotion.partner_id = partner.id
  and plays.promotion_id = promotion.id


SQL generated by Eloquent (a laravel PHP ORM)

select count(*) as aggregate 
from `plays` 
inner join `promotion` on `promotion`.`id` = `plays`.`promotion_id` 
where `promotion`.`partner_id` = 1



Is my version using inner out outer join?
is the inner join of the generated example better, or is it the same as my version?


There are 3 tables in this example:

plays
  int id
  int promotion_id

promotion
  int id
  int partner_id

partner
  int id


The sql is just to count all the plays which belong to a partner (through the promotion table)
The default join type is inner join.  

The second query may be better as it avoids an extra join to the partner table.  The required partner id value is available from the promotion table.  The impact will likely be minimal in this case. 

I would recommend prefixing the primary key id columns with the table name (singular form); play_id, promotion_id and partner_id.  Most design tools allow this, but may default to the form you have.

Learn to use explain plans to understand how the query will be executed.  This is not foolproof as the execution plan may be influenced by table sizes and other factors.  Different databases may generate different execution plans.