The Collaborative International Dictionary of English v.0.48:

League \League\ (l[=e]g), n. [F. ligue, LL. liga, fr. L. ligare
   to bind; cf. Sp. liga. Cf. Ally a confederate, Ligature.]
   1. An alliance or combination of two or more nations,
      parties, organizations, or persons, for the accomplishment
      of a purpose which requires a continued course of action,
      as for mutual defense, or for furtherance of commercial,
      religious, or political interests, etc.
      [1913 Webster]

            And let there be
            'Twixt us and them no league, nor amity. --Denham.
      [1913 Webster]

   2. Specifically: (Sports) An association of sports teams that
      establishes rules of play, decides questions of membership
      in the league, and organizes matches between the member
      teams. In some cases a sports league is called a
      conference, as in the National Football Conference.
      [PJC]

   Note: A league may be offensive or defensive, or both;
         offensive, when the parties agree to unite in attacking
         a common enemy; defensive, when they agree to a mutual
         defense of each other against an enemy.
         [1913 Webster]

   The Holy League, an alliance of Roman Catholics formed in
      1576 by influence of the Duke of Guise for the exclusion
      of Protestants from the throne of France.

   Solemn League and Covenant. See Covenant,2.

   The land league, an association, organized in Dublin in
      1879, to promote the interests of the Irish tenantry, its
      avowed objects being to secure fixity of tenure, fair
      rent, and free sale of the tenants' interest. It was
      declared illegal by Parliament, but vigorous prosecutions
      have failed to suppress it.

   Syn: Alliance; confederacy; confederation; coalition;
        combination; compact; cooperation.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Conference \Con"fer*ence\, n. [F. conf['e]rence. See Confer.]
   1. The act of comparing two or more things together;
      comparison. [Obs.]
      [1913 Webster]

            Helps and furtherances which . . . the mutual
            conference of all men's collections and observations
            may afford.                           --Hocker.
      [1913 Webster]

   2. The act of consulting together formally; serious
      conversation or discussion; interchange of views.
      [1913 Webster]

            Nor with such free and friendly conference
            As he hath used of old.               --Shak.
      [1913 Webster]

   3. A meeting for consultation, discussion, or an interchange
      of opinions.
      [1913 Webster]

   4. A meeting of the two branches of a legislature, by their
      committees, to adjust between them.
      [1913 Webster]

   5. (Methodist Church) A stated meeting of preachers and
      others, invested with authority to take cognizance of
      ecclesiastical matters.
      [1913 Webster]

   6. A voluntary association of Congregational churches of a
      district; the district in which such churches are.
      [1913 Webster]

   Conference meeting, a meeting for conference. Specifically,
      a meeting conducted (usually) by laymen, for conference
      and prayer. [U. S.]

   Conference room, a room for conference and prayer, and for
      the pastor's less formal addresses. [U. S.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

conference
    n 1: a prearranged meeting for consultation or exchange of
         information or discussion (especially one with a formal
         agenda)
    2: an association of sports teams that organizes matches for its
       members [syn: league, conference]
    3: a discussion among participants who have an agreed (serious)
       topic [syn: conference, group discussion]

Moby Thesaurus II by Grady Ward, 1.0:

143 Moby Thesaurus words for "conference":
   British Cabinet, Council of Nicaea, Council of Trent,
   Lateran Council, Sanhedrin, US Cabinet, Vatican Council,
   advisory body, airing, analysis, archbishopric, archdiocese,
   assembly, association, attention, audience, audition, bargaining,
   bargaining session, bench, bishopric, board, body of advisers,
   borough council, brain trust, bugging, bull session, buzz session,
   cabinet, camarilla, canvassing, chamber, chapter, circuit,
   city council, classis, colloquium, colloquy, common council,
   conciliarism, conclave, confab, confabulation, confrontation,
   congregation, congress, consideration, consistory, consultation,
   consultative assembly, convention, convocation, council,
   council fire, council of ministers, council of state,
   council of war, county council, court, debate, debating,
   deliberation, deliberative assembly, dialectic, dialogue, diet,
   diocesan conference, diocese, directory, discussion, divan, ear,
   eavesdropping, ecclesiastical council, ecumenical council,
   electronic surveillance, examination, exchange of views,
   eyeball-to-eyeball encounter, favorable attention, forum, hearing,
   high-level talk, huddle, interchange of views, interview,
   investigation, joint discussion, junta, kitchen cabinet,
   legislature, listening, listening in, logical analysis,
   logical discussion, loop, meeting, negotiations, news conference,
   open discussion, open forum, palaver, panel discussion, parish,
   parish council, parley, parochial church council,
   parochial council, plenary council, pourparler, powwow, presbytery,
   press conference, privy council, province, rap, rap session,
   review, round robin, round table, seance, see, seminar, session,
   sitting, soviet, staff, study, summit, summit conference, summitry,
   symposium, syndicate, synod, talk, town meeting, treatment,
   tribunal, tryout, ventilation, vestry, wheel, wiretapping



Bouvier's Law Dictionary, Revised 6th Ed (1856):

CONFERENCE, practice, legislation. In practice, it is the meeting of the
parties or their attorneys in a cause, for the purpose of endeavoring to
settle the same.
     2. In legislation, when the senate and house of representatives cannot
agree on a bill or resolution which it is desirable should be passed,
committees are appointed by the two bodies respectively, who are called
committees of conference, and whose duty it is, if possible, to -reconcile
the differences between them.
     3. In the French law, this term is used to signify the similarity and
comparison between two laws, or two systems of law; as the Roman and the
common law. Encyclopedie, h.t.
     4. In diplomacy, conferences are verbal explanations between ministers
of two nations at least, for the purpose of accelerating various
difficulties and delays, necessarily attending written communications.