Would you care to explain detailed the differences and relations between spirit, soul and body as seen from Hinduism? I read about 'atma', 'jivatma', 'chitta', 'chaitanya', 'supreme soul', 'anthakarana', 'manas', etcetera.
'Gezellig' is a typical Dutch word that in other languages actually does not know an adequate equivalent. In English for instance 'companionable' or 'cosy' may near the indication of what Dutch speakers consider to be 'gezellig',1 but as a one-to-one translation they still fall short. To really be able to understand what is meant with 'gezellig' English speakers have to know the context wherein the word is used and preferably have experienced themselves the Dutch 'gezelligheid'.
Now Hinduism and its sacred language, Sanskrit, have their own vocabulary. The Hindu's are a spiritual people2 and in Sanskrit we recognize those spiritual orientations in a very rich vocabulary for indication of spiritual principles, comparable to Eskimo's having many different words to indicate snow. And like it is difficult to translate the Dutch word 'gezellig' to English, it is often even more difficult to translate spiritual Sanskrit words to English.
To however bring the wisdom of the East to the West, disciples like Helena Blavatsky and Alice Bailey have under direction of their Eastern teachers still attempted to express Eastern wisdoms in Western words. The theosophy of Blavatsky aimed at being a synthesis of science, religion and philosophy, and the ageless wisdom of Bailey aimed at contributing to the establishment of a synthesized world religion.3, 4 Thereby they developed their own terminology, which makes use of Eastern terms like 'atma', 'buddhi' and 'manas' and Western terms like 'spirit', 'soul' and 'personality', but which thereby may still deviate from the traditional Eastern and Western use of those terms.
Let's take as example the term 'soul'. This Western term is in its generality often used as a translation for the Eastern term 'atma'.5 However agnostics use the term 'soul' often as indication of a human psyche which dies along with the body, while Hindu's see the atma as immortal and as one with the all-soul, with the 'paramatman'. And Christians then may believe too that the soul is immortal, however they consider it as created by and separated from God. So 'soul' cannot count as a one-to-one translation for 'atma',6 unless its definition, or that of 'atma', is changed. And in the teachings of Blavatsky and Bailey these terms are worked on and do shifts of interpretations take place.
Now the teachings of Bailey connect well to those of Blavatsky, however still we also find therein emphasis differences. And also within Hinduism in the many schools of teaching emphasis differences are to be found. Consider a colour spectrum that from the top to the bottom gradually goes from violet to red. This spectrum may be interpreted as consisting of the seven colours of violet, indigo, blue, green, yellow, orange and red, but also as consisting of the three colours of blue, yellow and red, or even as consisting of only blue and red. In that latter interpretation the term 'blue' has a much wider area of reference than in the first interpretation, while both interpretations still use the same term. The similarities are thus approximate and not exact. This goes mutatis mutandis also for Hindu terms.
Further the Hinduist Sanskrit terms are outermost numerous. So here we have to do with a very large collection of Hindu terms, which within the many different schools of Hinduism know interpretation differences, and which then would have to be translated into English terms, which themselves can also be interpreted diversely. This asks for very much explaining and a lot more space than is available here.
Actually, for who wants to understand Hindu terms from the Hindu perspective no other choice is left than to take a plunge into the deep and to immerse himself in the diverse Hindu teachings. And who then wants to be able to relate them to the terms of theosophy and the ageless wisdom of Blavatsky and Bailey will have to immerse himself also in those teachings.
It's a matter of zooming in and out to terms and their context and it's a matter of study and contemplation. Eventually all terminologies will drop away in an insignificance, however only at the end, and not at the beginning.7
Although one-to-one translations between Eastern and Western terms are thus not exact, nevertheless when this is taken into account a general overview can be given, at least in case of some of the Hindu terms. In this answer shall thereby mostly be connected to the translations as they are applied in the theosophy and ageless wisdom of Blavatsky and Bailey.
Bailey considers that man as a threefold consists of (1) spirit or a monad, (2) consciousness or a soul and (3) matter or a person. The soul is also considered to be threefold and to consist of (1) will, (2) intuition or love-wisdom and (3) abstract or higher thought. The person is again threefold and consists of (1) concrete or lower thought or a mental body, (2) emotion or an astral body and (3) a material or physical body. This physical body consists in its turn then of (1) a subtle physical or etheric or vital body and (2) a gross physical body.8, 9 In its generality it can be said that the spiritual monad works through the conscious soul, which works through the material person by means of incarnations. However like the soul is the mediating principle between the monad and the person, the soul and the person also know a mediating principle, namely the egoic body,10 which is placed between the higher and the lower mind. On this level we also find the mediating rainbow bridge.11
For both the spiritual monad and (especially) the highest principle of the conscious soul, the will, the Hindu term 'atma' is used.12, 13 For the intuition or the love-wisdom of the soul the Hindu term 'buddhi' is used. For the dual (higher and lower) mind 'manas' is used, and for the emotion or the astral body 'kama'. The subtle physical or etheric or vital body regards the 'prana'.14 The person regards the form, and this is called 'rupa', while the principles above it are formless and are called 'arupa'.15, 16 The mental body then may also be called 'manasarupa' ('manas-rupa'),17 the astral body 'kamarupa'18 and the subtle physical body 'pranarupa'. This type of word combinations are much found in Sanskrit. The egoic body is also called the 'karana sarira',19 and the rainbow bridge the 'antahkarana'20.
In the Samkhya teachings of Hinduism reference is made to the gross physical body with the term 'annamayakosha', which can be literally translated as 'illusionary food cover'. The subtle physical body is named there 'pranamayakosha', or the 'illusionary vitality cover'. There is also a 'manomayakosha' (the 'illusionary manas' or 'thought cover'), a 'vijnanamayakosha' ('illusionary wisdom cover') and an 'anandamayakosha' ('illusionary bliss cover'). These covers cover the 'purusha', which regards the spirit or the soul.21 In this overview the purusha corresponds loosely with the atma, anandamayakosha with buddhi as intuition or love-wisdom, vijnanamayakosha with buddhi-manas as the higher, abstract mind, manomayakosha with manas as the lower, concrete mind, pranamayakosha with the subtle physical or etheric or vital body and annamayakosha with the gross physical body. The 'antahkarana' contains in the Samkhy teaching buddhi and manas, but also 'ahamkar', which regards the notion of the personal 'I'.
Regarding the terms in the question the following can be said. 'Jivatma' consists of the words 'jiva' and 'atma', whereby 'jiva' refers to a living being. Loosely translated a jivatma thus regards an individual soul. There is also a paramatman, which regards the all-soul, with which all jivatma's are one.22 This is the 'supreme soul'. 'Chaitanya' rather refers to consciousness as such, but it is also the name of an important Hindu master.23 'Chitta' regards the mind stuff.24
Hopefully this answer can give a little push in the right direction.