Krashen's i+1
Krashen's view is that language development takes place only through reception of comprehensible input. If i is the current level of a learner's language, she needs to receive comprehensible input at i+1 in order to acquire that language along natural order. If communication takes place using i+1, Language Acquisition Device (LAD) will act and assimilate the langauge received, contributing to language acquisition.
Vygotsky's Zone of Proximal Development (ZPD)
According to Vygotsky, Zone of Proximal Development (ZPD) is the the area between the actual developmental stage of an individual where she solves problems independently, and the potentisl developmental stage where she solves problems with the help of a more capable peer/adult (Vygotsky, 1978, p. 36). ZPD represents the scope of a learner in terms of development, where functions are in the process of maturation. It does not reside within the learner, but is a meeting place of all elements and aspects of the learning process (learner, teacher, learning materials, context, motivation, etc.).
Historical Context of ZPD
Children's IQ was determined by observing their independent problem solving abilities. But once at school, some children with high IQ scores showed a lower IQ, whild those with a lower IQ showed an increase. To address this issue, Vygotsky talked about the upper limit of possible development in the child. He argued that this upper limit could be determined by observing the child's problem solving skills when an adult's help is available. This means, while all children may appear to have the same level of IQ, some may have a higher upper limit than the others. Those with the higher upper limit will be able to comfortably move up their IQ score to the upper limit. Those with the lower upper limits will not be able to meet this level of development because the potential for development was lower. In other words, some children have a smaller potential for development, while some have a higher one. This area or potential for IQ development is what Vygotsky called ZPD.
The implication is that if a child has a high IQ but small ZPD, it may show less development than a child who has lower IQ, but a larger ZPD. Exposure to and familiarity with knowledge may help some children to scale most of their ZPDs without instruction. And when instruction is provided, they may show lower development than others because they have already used the potential offered by their ZPDs.
Note that for Vygostky, instruction and learning could be forerunners of development. He criticized the claim that development is impervious to instruction. Learning paves the way for development to occur. However, we should not assume that in ZPD, either is a precondition for the other. In ZPD, learning and development act together, or learning leads to development. Vygotsky has shown in his experiments that children learn in interaction and that leads to development.
Learning and Development
Vygotsky and Krashen are different in terms of how they see development. Vygotsky sees the process of development as maturing of features. Krashen sees whether or not a feature is acquired or not. i is what is acquired, and i+1 is what is to be acquired next. Vygotsky on the other hand makes predictions about what is in the process of maturing or developing. Krashen's theory deals with stages that follow a yes-or-no approach to development; there is no place for the process of maturing. In addition, Krashen's development is clear-cut and predictable, while Vygotsky sees many intervening factors in the process, making prediction of a definite linguistic future impossible.
Kashen's position is that learning and development are separate. Even when learning is seen as helpful to acquire knowledge of language use, he sees it as different from acquisition. Learned knowledge is different from acquired knowledge. If not through comprehensible input, it is not acquisition. Consequently, he was against syllabuses that used a natural acquisition order. Vygotsky sees learning and development as a unity.
Theoretical differences
Krashen sees the learner as an individual, separate from 'others'. The learner can learn in isolation from the society provided she receives comprehensible input and has a Language Acquisition Device (LAD). Language production is not improtant in his scheme, even when he acknowledges that interaction may help acquisition process. Therefore, there is no place for social interaction in Krashen's theory of SLA. This is because Krashen subscribes to the view of language as a scientific object of study, which ensues from Saussure's concepts where language is a natural phenomenon, separate from human interactions and activities. Hence for Krashen, there is no need to talk about human interactions in langauge acquisition. This is a pure or hard scientific view of language and language acquisition where learner's individuality does not have an influence on learning and acquisition.
Vygotsky's theory is founded on the view that the individual is based in the society which is based in a culture. This view rejects the view that individuals are independent entities, and that learning is an individual activity. For Vygotsky, mental activities are the result of socio-historically situated act of living, performed by individuals who are part of a society and culture situated in a time frame. All language interactions therefore have a concrete context. Making sense of langauge for children therefore, is to discover and use the same tools that made the message they try to make sense of. For second language learners, it is the same attempt to make meaning out of a new langauge. This is a form of establishing an identity, and regulate the self. This is an organic process situated in the society and culture in which learning and interacton takes place. This is radically different from the input hypothesis of Krashen. This is a softer or romantic-scientific view of language and language acquisition, where learner is a cultural agent situated in a specific context. 
