There may be a correlation between strength and size but no direct causation. Many lilliputian sized Olympic lifters continue to gain strength year after year despite the fact their body mass remains the same. On the other hand there are hulking bodybuilders who are not as strong as they look. This is why in "Strongman Contests" you rarely ever see a bodybuilder win. The strength of a muscle is certainly proportional to its size, however there are many other factors from which absolute strength is determined
The number of muscle fibers actually contracting
The speed at which these muscle fibers are contracting
The amount of inhibitory motor neurons active
The duration of time a muscle fiber can sustain the contraction
The order of muscle contraction
Recruitment of stabilizing and co-contracting muscles
The volitional (motivation) effort put forth
The amount of human growth hormone and testosterone present in the blood stream -women usually produce small amounts of these hormones which prevent her muscles from becoming 'too big'.
Different training modalities are used for increasing strength or hypertrophy (size). Neuromuscular efficiency is paramount in producing strength which is strongly influenced by regular explosive exercise. Strength training is characterized by maximal or close to maximal lifts, low time under tension 5-20 seconds (the time it takes to perform a set) and high in between rest periods. Whereas hypertrophy training is dependent upon longer bouts of time under tension, about 35-70 seconds, low rest periods and weights not typically exceeding 80% of one's max. By changing the variables and closely monitoring one's routine and progress it is possible to develop a training routine targeting strength, size or a hybrid combination of the two.
When compared with strength training, bodybuilding has fewer real world applications. Strength training depends on lots of muscles engaged using momentum, leverage and speed whereas building muscle size focuses on controlled slow movements with with a clear emphasis on individual muscles. Functional movement patterns are not the domain of bodybuilders. Olympic lifts and low reps are usually fast and have global body demands. Many people workout to look better but neglect the more primal aspect of exercise, strength. Depending on your goals and limitations it might be wise to incorporate a hybrid training regimen that covers all bases.
The Pocket Hercules, Naim Suleymanoglu, from Greece is 4'10" tall and weighs less than 135lbs yet he was strong enough to clean and jerk over 415lbs! He is a great example of someone who is quite small who posses hulking strength.