First two truths are relate to "samsara". But how 3rd and 4th truths relate to Pratītyasamutpāda?
If we divide Pratītyasamutpāda to three existences it's much easier to explain. (this can be explained for each moment as well)
1. Ignorance 2. Formations
3. Consciousness 4. Nāma-rūpa 5. The six senses 6. Touch 7. Sensation
12. Old age and death
- If we take second existence as the current life, points 3, 4, 5, 6, and 7 (consciousness, nāma-rūpa, the six senses, touch and sensation) are another form or representation of the five aggregates which is same as suffering or the first noble truth.
- If you crave for the sensations (nourished by ignorance) in this existence, then this will form your next life. Although craving, clinging, becoming, ignorance and formations in this life are all causes for the next life, craving is the main culprit, hence craving becomes the second noble truth.
- If craving is ceased in this very life, there won't be another existence,that means you've overcome the suffering, this can be achieved and has been achieved, hence this becomes the third noble truth.
- To realise this, you have to follow the eightfold path, which is the fourth noble truth. However, Pratītyasamutpāda doesn't straight away relate to the fourth noble truth as the other three here.
The teaching of Dependent Origination is part of what is known as the Middle Teaching (majjhena-dhammadesana). It is taught as an impersonal, natural truth, a description of the nature of things as they are, avoiding the extreme theories or biased views that human beings are want to fall into as a result of their distorted perceptions of the world and their attachments and desires within it. The cycle of Dependent Origination which describes the problem of human suffering comes in two limbs: the first limb, called the samudayavara (origination mode), is a description of the arising of suffering, corresponding with the second Noble Truth, the cause of suffering; the second limb, called the nirodhavara (cessation mode), is a description of the cessation of suffering, corresponding with the third Noble Truth.
The 3rd and 4th truths do not relate to Pratītyasamutpāda. Instead, the relate to Pratītyanirodha. In other words, the 3rd and 4th truths end/destroy Pratītyasamutpāda.
Pratītyasamutpāda is the 2nd noble truth explained with more detail (quoted below).
When the Buddha gave the 1st sermon on the 4 noble truths, this was simply an introductory or beginners teaching & not the Dhamma in full.
In summary, there is no difference between the 4 noble truths & Pratītyasamutpāda/Nirodha, apart from the 4 noble truth is a short version & Pratītyasamutpāda/Nirodha is a long version.
"And what is the noble truth of stress? Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, & despair are stressful; association with what is not loved is stressful, separation from what is loved is stressful, not getting what is wanted is stressful. In short, the five clinging-aggregates are stressful. This is called the noble truth of stress.
"And what is the noble truth of the origination of stress?
"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. From clinging as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then old age & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of stress & suffering.