PM: The Prime Minister. The head of the government and the person who selects all the other ministers. Of course, in this era of coalition governments, that power of selection is vastly curtailed and individual party chiefs have a greater say.
CPP: Congress Party in Parliament. Collection of all Congress members of the Lok Sabha and the Rajya Sabha. It is the leader of this group who becomes PM when the party has a majority in the Lok Sabha, not the party president. That's in theory, of course. In most cases, the two posts are held by the same individual.
CWC: Congress Working Committee. Highest decision-making body of the Congress party. (Of course, the party president ranks higher, but that's a different story.) All policy decisions in the party have to be taken by the CWC. It usually does as advised by the party president.
CPI-M Politburo: A committee of top leaders that is empowered to take political and organisational decisions between two sittings of the central committee, highest decision-making body of the Marxist party.
CLP: Congress Legislature Party. The state assembly version of the CPP. Almost never elects its own leader, leaving the choice to the 'high command' (the president). When it does, it is under the 'guidance' of the president with a couple of 'observers' ensuring there are no ugly surprises.