The passage in the question is also found in AN 4.171. The translation in the questions appears highly questionable. In the passage are the Pali words:
paṭilābho = acquisition of. For example, 'paṭilābho' is used in:
SN 55.1 about obtaining the four factors of stream-entry;
AN 8.2 about obtaining the wisdom fundamental to the holy life;
AN 4.171 about acquiring individual character (attabhava);
MN 106 about obtaining equanimity;
SN 42.8 about acquiring a view;
Dhp 333 about acquisition of wisdom.
attabhāva = individual character or self-nature or state of individuality. For example, 'attabhava' is used in:
Staying alone, the forests seem to rob the mind of a monk who isn’t immersed in samādhi. If someone should say this: ‘Though I don’t have immersion, I’m going to frequent remote lodgings in the wilderness and the forest.’ You can expect that they’ll sink down or float away.
Suppose... along comes a rabbit or a cat. They’d think: ‘What difference is there between me and a bull elephant? Why don’t I plunge into this lake and play around while washing my ears and back? When I’ve bathed and drunk, I’ll emerge from the water and go wherever I want.’ They jump into the lake rashly, without thinking. You can expect that they’ll sink down or float away. Why is that? Because their small individual nature (attabhāvo ) finds no footing in the depths.
AN 10.99
Both Thanissaro & Bhikkhu Bodhi translate this verse differently. Thanissaro translates as:
Four acquisitions of a self-state [atta-bhāva]: Friends, there is the acquisition of a self-state where one goes to a self-state through one’s own intention & not through the intention of another. There is the acquisition of a self-state where one goes to a self-state through the intention of another & not through one’s own intention. There is the acquisition of a self-state where one goes to a self-state both through one’s own intention & through the intention of another. There is the acquisition of a self-state where one goes to a self-state neither through one’s own intention nor through the intention of another.
Therefore, the quote from DN 33 appears to say:
Four kinds of acquisition of self-nature/individual character (cattāro attabhāvapaṭilābhā).
There is acquisition of self-nature/individual character where only one’s own intention is effective, not that of others.
There is acquisition of self-nature/individual character where only the intention of others is effective, not one’s own.
There is acquisition of self-nature/individual character where both one’s own and others’ intentions are effective.
There is acquisition of self-nature/individual character where neither one’s own nor others’ intentions are effective.
For example:
I feel my life has lost meaning and, contrary to the wishes of my family, friends & employer, I decide to travel around the world searching for the meaning of life. This is an example of acquisition of individual character based on my intentions alone.
I feel my life has lost meaning & think about travelling around the world searching for the meaning of life. However, my family, friends & employer oppose my idea and my employer offers to double my salary if I stay home & continue working for them. Against my deeper wishes, I follow the wishes of my employer & family. This is an example of acquisition of individual character based on the intentions of others.
I feel my life has lost meaning and, contrary to the wishes of my family, friends & employer, I decide to travel around the world searching for the meaning of life. In my travels, I visit a monastery and a benevolent teacher of Dhamma offers me detailed instructions and properly supervises me as his student. I devote my mind to following the instructions of the benevolent teacher & my mind enters the Path and finds satisfaction. This is an example of acquisition of individual character based on the intentions of both myself and another (the teacher).
My mind enters the jhanas and the mental faculty of intention is suspended. The five lower faculties are eradicated and the mind is spontaneously arisen as a Non-Returner. This is an example of acquisition of individual character based on the neither the intentions of both myself and another (the teacher).