The Collaborative International Dictionary of English v.0.48:

Variance \Va"ri*ance\, n. [L. variantia.]
   1. The quality or state of being variant; change of
      condition; variation.
      [1913 Webster]

   2. Difference that produces dispute or controversy;
      disagreement; dissension; discord; dispute; quarrel.
      [1913 Webster]

            That which is the strength of their amity shall
            prove the immediate author of their variance.
                                                  --Shak.
      [1913 Webster]

   3. (Law) A disagreement or difference between two parts of
      the same legal proceeding, which, to be effectual, ought
      to agree, -- as between the writ and the declaration, or
      between the allegation and the proof. --Bouvier.
      [1913 Webster]

   4. (Statistics) The expected value of the square of the
      deviation from the mean of a randomly distributed
      variable; the second moment about the mean. This is also
      the square of the standard deviation.
      [PJC]

   At variance, in disagreement; in a state of dissension or
      controversy; at enmity. "What cause brought him so soon at
      variance with himself?" --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

variance
    n 1: an event that departs from expectations [syn:
         discrepancy, variance, variant]
    2: discord that splits a group [syn: division, variance]
    3: the second moment around the mean; the expected value of the
       square of the deviations of a random variable from its mean
       value
    4: a difference between conflicting facts or claims or opinions;
       "a growing divergence of opinion" [syn: discrepancy,
       disagreement, divergence, variance]
    5: the quality of being subject to variation [syn:
       variability, variableness, variance] [ant:
       invariability, invariableness, invariance]
    6: an official dispensation to act contrary to a rule or
       regulation (typically a building regulation); "a zoning
       variance"
    7: an activity that varies from a norm or standard; "any
       variation in his routine was immediately reported" [syn:
       variation, variance]

Moby Thesaurus II by Grady Ward, 1.0:

107 Moby Thesaurus words for "variance":
   agreement to disagree, alienation, antagonism, apostasy, argument,
   argumentation, at variance, change, clashing, conflict, contention,
   contradiction, contrariety, contrast, controversy, counter-culture,
   cross-purposes, debate, departure, deviation, difference,
   difference of opinion, difficulty, disaccord, disaccordance,
   disagreement, disapprobation, disapproval, disconformity,
   discongruity, discord, discordance, discordancy, discrepancy,
   discreteness, disharmony, disparity, dispute, dissatisfaction,
   dissension, dissent, dissentience, dissidence, dissimilarity,
   dissonance, distinction, distinctness, disunion, disunity,
   divergence, divergency, diversity, dividedness, division,
   dropping out, faction, far cry, fluctuation, heterogeneity,
   in disagreement, in dispute, inaccordance, incompatibility,
   incongruity, inconsistency, inconsonance, inequality,
   inharmoniousness, inharmony, irreconcilability, jarring,
   minority opinion, misunderstanding, mixture, negation,
   nonagreement, nonassent, nonconcurrence, nonconformity, nonconsent,
   odds, opposition, oppugnancy, otherness, polarization, quarrel,
   recusance, recusancy, rejection, repudiation, repugnance, rift,
   schism, secession, separateness, separation, severing, strife,
   unconformity, underground, unharmoniousness, unlikeness,
   unorthodoxy, variation, variegation, variety, withdrawal



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

VARIANCE, pleading, evidence. A disagreement or difference between two parts
of the same legal proceeding, which ought to agree together. Variances are
between the writ and the declaration, and between the declaration and the
evidence.
     2.-1. When the variance is a matter of substance, as if the writ sounds
in contract, and the other in tort, and e converso, or if the writ demands
one thing or subject, and the declaration another, advantage may be taken of
it, even in arrest of judgment; for it is the writ which gives authority to
the court to proceed in any given suit, and, therefore, the court can have
no authority to hear and determine a cause substantially different from that
in the writ. Hob. 279; Cro. Eliz. 722. But if the variance is in matter of
mere form, as in time or place, when that circumstance is immaterial,
advantage can only be taken of it by plea in abatement. Yelv. 120; Latch.
173; Bac. Ab. Abatement, I; Gould, Pl. c. 5, Sec. 98 1 Chit. Pl. 438.
     3.-2. A variance by disagreement in some particular point or points
only between the allegation and the evidence, when upon a material point, is
as fatal to the party on whom the proof lies, as a total failure of
evidence. For example; the plaintiff declared in covenant for not repairing,
pursuant to the covenant in a lease, and stated the covenant, as a covenant
to "repair when and as need should require;" and issue was joined on a
traverse of the deed alleged. The plaintiff at the trial produced the deed
in proof, and it appeared that the covenant was to "repair when and as need
should require, and at farthest after notice:" the latter words having been
omitted in the declaration. This was held to be a variance, because the
additional words were material, and qualified the effect of the contract. 7
Taunt. 385. But a variance in mere form or in matter quite immaterial, will
not be regarded. Str. 690. Vide 1 Vin. Ab. 41; 12 Vin. Ab. 63; 21 Vin. Ab.
538 Com. Dig. Abatement, G 8, H 7; Id.; Amendment, D 7, 8, V 3: Bail, R 7;
Obligation, B 4; Pleader, C 14, 15, L 24, 30; Record, C, D, F; Phil. Ev.
Index, 11. t. Stark. Ev. Index, h.t., Roscoe's Ev. Index, h.t.; 18 E. C. L.
R. 139, 149, 153 1 Dougl. 194; 2 Salk. 659; Harr. Dig. h.t. Chit. Pl. Index,
h.t.; United States Dig. Pleading II, d and e; Bouv. Inst. Index: h.t.