What is the difference between anger and frustration?

Anger (kodho) arises out of the cravings of identity view and is described as:

AN7.64:10.1: An angry person kills with body or speech; overcome with anger, they lose their wealth.

Frustration (bhāgī assa) arises out of lack of progress:

AN4.77:1.1: “Mendicants, these four things are unthinkable. They should not be thought about, and anyone who tries to think about them will go mad or get frustrated. What four? The scope of the Buddhas … The scope of one in absorption … The results of deeds … Speculation about the world …

They are both unskillful, but frustration is milder in that one may be frustrated in practice towards a noble goal. Anger, on the other hand should be killed:

SN2.3:3.5: The noble ones praise the slaying of anger, for when it’s incinerated there is no sorrow.”

I think what you meant by anger is dvesha. And I think what you meant by frustration is sorrow, lamentation, pain, distress.

In buddhism dvesha is a reason which results frustration. I'll explain this in detail.

Below is a quote from Paticca-samuppada-vibhanga Sutta.

From ignorance as a requisite condition come fabrications. From fabrications as a requisite condition comes consciousness. From consciousness as a requisite condition comes name-&-form. From name-&-form as a requisite condition come the six sense media. From the six sense media as a requisite condition comes contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of stress & suffering. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of stress & suffering.

1. Above quote clearly shows that Ignorance causes the frustration.

2. What's ignorance? Most people simply says that it's not knowing of 4 noble truth. But let's try to get another view of this from the cannon.

Not knowing the gratification (assada), the danger (adinava) and how to escape from (nissarana) the five aggregates (rupa, vedana, sangna, sankara, vingnana) is called Avidya (ignorance)

Above is my translation of Majjhima Nikaya-3 -> Avijja vagga -> Patama Assada Sutta (Sorry I couldn't find any english reference on this, if any one found let me know) in Sinhala/Pali Cannon. And I'm not a professional translator, excuse me for any concerns with my words here. These definitions are not popular Dhamma, but if you look closely this is clearly explained in many places in cannon. I've added quote from Cula-sihanada Sutta at the end of the answer for anyone interested to have a look

So by now we have evidences to say frustration is caused by ignorance and ignorance is the fact that not knowing assada, adinava and nissarana of five aggregates. And also we know that the path to Nivana is uprooting avijja (ignorance). Now let's see the definition of Ultimate (Nivana) from another angle.

Below is a quote from Asaṅkhata Saṁyutta (SN 43) which gives the definition of Nivana (ultimate)

The Blessed One said, “Which, monks, is the ultimate? Whatever is the ending of passion, the ending of aversion, the ending of delusion: This is called the ultimate.

Here aversion means dvesha. One point to highlight is that we are talking about the same thing but in different angles.

So ignorance is the main cause, uprooting ignorance -> results in Nivana. And by ending passion, aversion and delusion also results in Nivana. In the absence of these passion, aversion and delusion the ignorance get uprooted. And these passion, aversion and delusion are risen as a result of not knowing the assada, adinava and nissarana of the five aggregates. And due to this unknown we continue the paticcasamuppada cycle which starts with ignorance (dvesha=anger is one of the requisite condition type) and results in death, sorrow, lamentation, pain, distress.. (Same thing happens with all passion, aversion and delusion. I won't talk about these in detail here)

(Knowing assada, adinava and nissarana of five aggregates means understanding the four noble truth.)

So, simple answer to your question is,

Anger (dvesha) causes to results in frustration.

Below is quote from Cula-sihanada Sutta just for the reference. And don't forget to read the foot-note 6 of the below quote

7. "Any recluses or brahmans who do not understand as they actually are the origin, the disappearance, the gratification, the danger and the escape6 in the case of these two views are affected by lust, affected by hate, affected by delusion, affected by craving, affected by clinging, without vision, given to favoring and opposing, and they delight in and enjoy proliferation. They are not freed from birth, aging and death, from sorrow, lamentation, pain, grief and despair; they are not freed from suffering, I say.

8. "Any recluses or brahmans who understand as they actually are the origin, the disappearance, the gratification, the danger and the escape in the case of these two views are without lust, without hate, without delusion, without craving, without clinging, with vision, not given to favoring and opposing, and they do not delight in and enjoy proliferation. They are freed from birth, aging and death, from sorrow, lamentation, pain, grief and despair; they are freed from suffering, I say. [66]

Speaking from a kind of buddhist perspective on psychology, anger and frustration represent emotional reactions to different types of attachments.

Anger is usually a response to a perceived external injury to an identity-object. In other words, one has an identity attachment to something — be it one's self, a loved one, a favorite book or tool or rug, etc — and one perceives that another person or thing has caused insult or injury to it. Someone sits in your favorite chair and the chair leg breaks; anger arises at that someone because they ostensibly 'caused' the loss of that attached identity.

Frustration, by contrast, is usually a response to a perceived obstacle. In other words, one has an identity attachment to a goal, desire, or achievement, and one becomes frustrated that it is not easily or immediately achieved. One wants to be a concert pianist, but discovers that the dexterity required is just out of their reach; frustration arises at the inability to achieve the attached goal.

It would make sense that monastics would be more prone to frustration than anger. They are instructed early to release attachments to any identity-objects, so they will be less prone to react to insult or injury to that which they have already determined to let go of. But releasing attachments to goals and aspirations is a more difficult project, particularly early on when monks have explicitly set the goal of monastic attainment. Frustration at one's failure to grasp the principles of the faith would be a normal occurrence in a monastic setting.

To quote Yvan Amar: "Peace is happiness at rest. Happiness is peace in motion"...

I'd say "Frustration is resistance at rest. Anger is resistance in motion". With resistance always coming from attachment.

I agree with Ted Wrigley in a previous answer, monastics (and most people actively in a spiritual path) first master the outward facing (anger). The inward facing (frustration) takes much more work and dedication.

If I remember correctly my Abhidharma lectures, both anger and frustration are the types of aversion. Anger is how aversion manifests when you feel that you are stronger than the object of your aversion, while frustration is when you feel weaker than the object/cause of aversion.