Not the same thing, and as has been said already the difference between them is motivation and intent of the actions vs result. (Well put)

I might argue meaning is more of a state of being, as are most emotions we try to unsuccessfully dissect. I belive you could even break it down to responsibility + usefullness = meaning.

When you are conscious of mind and bring awareness to your inherent responsibilities and find ways to follow those responsibilities down a useful path meaning would be a naturally occurring result.

I think there are responsibilities that are akin to needs vs want. This falls back to intent, you can take on responsibilities you shouldn't or don't have to and they could be useful or not. That depends on your intent. Was it done for selfish gain, did it "kill to birds with one stone" and you reason that even though it was selfish it was still useful to others? This likely wouldn't create as much meaning as something done for a greater nessesity.

Like other things in life need should come before want. Our culture is confused trying to understanding the difference at large. Marketing has really blurred the lines here and so finding meaning is hard for most because they are seeking to fill wants and often put off nessesity.

On the other hand if you manage your energy and focuse on need, what is left over can help push you forward into seeking out the special impact you can chose (want) to have on the world vs need would equate to a sort of "destiny". When people deny what path life has put them on they are denying their inherent responsibilities and never get to the wants that would really create meaning in their lives.

Okay, I'll bite.

1. No.

Responsibility is the acceptance that you have to do (or not do) something. That something is always considered useful to someone, like picking the kids up after school or building a house or judging a court case. It doesn't have to turn out to be useful, but it has to be considered useful by someone. For instance, an idiot brother might ask you to take on the responsibility of watching out for your parents coming up the stairs while he watches porn, a bank robber may ask you to take responsibility for having the getaway car there on time.

Being useful means doing something of value, which implies a valuer who gains use/value from the action. Taking the examples above, the actions were thought to be useful for, or of value to: the kids, the housed, the society, the brother and the bank robber, even if, in the final analysis, the latter two may be judged of no use/value at all.

The difference is that responsibility refers to the motivation and intent of the actions whereas usefullness refers to the results of the actions. If you picked up the kids or the bank robber because you happened to be passing by you would be just as useful but no responsibility would be involved.

2. The meaning of "meaning" has been complicated by the way Jordan Peterson uses it.

In normal use "meaning" means something like an elaboration of the definition. The sun going down means it will soon be dark. The tycoon means business. The meaning of spring is re-birth. What he really means when he says it was a great game is that his team won.

But the way Peterson uses Meaning is to make it into some sort of transcendental state of being. But I have yet to discover where he has explained the meaning of that state - which is a bit surprising given its cenral role in his thesis and his rule about being precise in speech. As best as I can understand it, Peterson's meaning of Meaning involves having a purpose and reducing suffering and it is a substitute for happiness or heaven. But what purpose? The suffering of whom? Why not happiness? Because it's too fragile? why not un-fragile happiness? There's more to this that needs a more precise explanation.

But to finally get to your question. Neither responsibility or usefulness creates meaning. But since both have something to do with Peterson's Meaning, I'd say responsibility creates more because it goes to intent and state of mind.

People who are responsible for their lives or jobs are usefulto themselves or others.

People who are used for purposes they do not understand are useful but may not be responsible.

I think there is an unspoken heirarchy here.

If actions do not have consequences, then there is nothing to be responsible for. Consequences infer responsibility. If there is no responsibility for actions, no actions can be useful.

I am using responsibility as a synonym for causation

1. Definitely not the same thing. Responsibility, to me, refers to accountability. Taking on responsibilities, and being accountable for your actions /decisions. Being useful, refers to your abilities, and how they can be used in a specific situation. Plenty of people have useful skills, but cannot be counted on. Usefulness is also subjective. You may be useful for mental tasks, but useless for manual labor. Or, vice versa.

2. You need both. If someone isn't responsible, you can't always count on them to follow through.

Parable of the Talents - For the non-religious just think of the Master as nature and don't read the last verse.

[biblegateway.com]

To answer question 1, no they are not the same. As for number 2, wouldn't you say that could possibly be determined by each individual? One person may put more value on responsibility, while another may put more importance on anything that could be useful to them. Differences between them? Responsibilty is a personal trait more or less, and whether something is useful or not is a personal choice.