Charged for both satellite and streaming over a year

You have to call DTV to cancel there is no other way, been that way since they started. It maybe possible to get back 60 days as that is all DTV gives you to dispute a bill.  You didn't switch to stream they are to separate services.  So why did it take a year to notice?

The only way to cancel DirecTV is to call. At the voice prompt you say "cancel" to route you directly to the retention/cancellation department.

DirecTV and DIRECTV STREAM are two separate providers. There is no migration from one to the other. Though both owned by AT&T (and now with the new co-owner), they have nothing to do with each other. It is treated the same as if it were DirecTV and either Netflix or Hulu, in that you cancel one and go to the other or have both if you really want to.

Chat is only supplmental to customer support. Their options are limited and certainly cannot cancel the account. Customer support does not get any record of the chat transcripts. Unless you kept your own copy, they are essentially gone.

Like most companies, DirecTV has a limited window (typically 60-90 days) for a billing dispute. Though the chat agent is at fault for intially providing wrong info, not noticing you were making separate payments every month for over a year is unfortunately your responsibility.

At this point, the only chance you have to resolve this in your favor is to file a BBB complaint. That sends the situation to the corporate level. This is no guarantee they will have a transcript to pull or that it will be an answer you want, but it is a shot. Just be prepared they could very well rule that you didn't call to cancel and so closing the account is all that can be done.

Regardless of the outcome, going forward I would be more attentive to your finances. When you start or cancel a service, or even make changes to what you have, review the following two bills at minimum (including the account the payments go from). That way you can see the change as expected, possibly with any prorated charges or credits, and then the normal bill going forward. In your situation that would have caught you were making two payments monthly and would have saved a lot of cost by addressing it in a reasonable time. Just a suggestion to avoid a similar or worse situation in the future.

How did I login into my “satellite” account, chat with an agent who then signed me up for streaming, and told me how to return my equipment, if they are two different agencies?  That is (Edited per community guidelines) my friend. 

Chat support itself seems to be a bit general. But yes, they are two separate entities under the same parent owner. There is no migration, so if someone drops satellite for streaming while under a service agreement, they pay an early cancellation fee (ECF) as they are canceling a provider. And that is why someone could have both (though that wouldn't be common).

Knowing how (supposedly) equipment return works, doesn't change the fact that they have never had the option to cancel DirecTV online. You have to call and speak with the cancellation department.

I agree that the chat agent greatly mislead you. But again, this could have been resolved with higher chance in your favor if it hadn't taken you over a year to notice the issue with your payments. With how much time has passed and customer support (including retention/cancellation) doesn't get the chat transcripts, a BBB complaint is the remaining option.

How did I login into my “satellite” account, chat with an agent who then signed me up for streaming, and told me how to return my equipment, if they are two different agencies?

Not two separate agencies. Directv Stream and Directv satellite are two separate products which share chat support. The chat agent should have known you needed to call to cancel satellite service, though. How do you not notice you are paying for satellite for a full year? Do you not review credit card or bank charges?

@Mchjo42

Use this link to contact customer support 

Contacts | AT&T (att.com)