They are one and the same. The Civil Service is the UK term for what is called Public Service in Australia...both are government employement.
Though it is so as above, here in India the definition of "Public Service" has been enlarged by the THE PREVENTION OF CORRUPTION ACT , 1988 (Central Act No.49\1988).
As per the above act the term "Public Service" is defined in clause 2 as..
2. Definitions: - In this Act, unless the context otherwise requires.-
(a) "Election" means any election, by whatever means held under any law for the purpose of selecting members of Parliament or any Legislature, local authority or other public authority;
(b) "Public Duty" means a duty in the discharge of which the State, the public or the community at large has an interest;
Explanation,- In this clause "State" includes a Corporation established by or under a Central, Provincial or State Act, or an authority or a body owned or controlled or aided by the Government or a Government company as defined in Section 617 of the Companies Act, 1956 (1 of 1956);
(c) " Public Servant " means.-
(i) any person in the service or pay of the Government or remunerated by the Government by fees or commission for the performance of any public duty;
(ii) any person in the service or pay of a local authority ;
(iii)any person in the service or pay of a Corporation established by or under a Central , provincial or State Act, or an authority or a body owned or controlled or aided by the Government or a Government Company as defined in Section 617 of the Companies Act , 1956 (1 of 1956)
(iv) any judge, including any person empowered by Law to discharge, whether by himself or as a member of anybody of persons, any adjudicatory functions;
(v) any person authorized by a court of justice to perform any duty, in connection with the administration of justice, including a liquidator, receiver or commissioner appointed by such court.
(vi) any arbitrator or other person to whom, any cause or matter has been referred for decision or report by a court of justice or by a competent public authority.
(vii) any person who holds an office by virtue of which he is empowered to prepare , publish , maintain or revise an electoral roll or to conduct an election or part of an election;
(viii) any person who holds an office by virtue of which he is authorised or required to perform any public duty;
(ix) any person who is the president, Secretary or of other office bearer of a registered co-operative society engaged in agriculture, industry, trade or banking, receiving or having received any financial aid from the Central Government or a State Government or from any Corporation established by or under a Central, provincial or State Act, or any authority or body owned or controlled or aided by the Government or a Government Company as defined in Section 617 of the Companies Act, 1956 (1 of 1956);
(x) any person who is a Chairman, member or employee of any Service Commission or Board, by whatever name called, or a member of any selection committee appointed by such Commission or Board for the conduct of any examination or making any selection on behalf of such Commission or Board;
(xi) any person who is a Vice-Chancellor or member of any governing body , professor, reader, lecturer or any other teacher or employee, by whatever designation called, of any University and any person whose services have been availed of by a University or any other public authority in connection with holding or conducting examinations;
(xii) any person who is an office bearer or an employee of an educational, scientific, social , cultural or other institution, in whatever manner established, receiving or having received any financial assistance from the Central Government or any State Government or local or other public authority.
Explanation 1- persons falling under any of the above sub-clauses or public servants whether appointed by the Government or not.
Explanation 2- Wherever the words "Public Servant" occur, they shall be understood of every person who is in actual possession of the situation of a public servant,
Whatever legal defect there may be in his right to hold that situation.