Implicit Learning vs. Latent Learning Sawyer (2005) defines "Implicit Learning" as:


  Implicit learning refers to situations in which complex information is acquired effortlessly (without a  conscious effort), and the resulting knowledge is difficult to express verbally (e.g., Berry, 1997; Cleeremans, Destrebecqz, &amp; Boyer, 1998; Reber, 1967 ). Although many types of implicit learning exist, a common process underlies most of them - the rapid, effortless, and untutored detection of patterns of covariation among events (Reber, 1993). (Page 19)


Also, this Wikipedia article provides a nice definition of it.

Soderstrom and Bjork (2015) have defined "Latent learning" as:


  Latent learning is defined as learning that occurs in the absence of any obvious reinforcement or noticeable behavioral changes. Learning is said to be “latent,” or hidden, because it is not exhibited unless a reinforcement of some kind is introduced to reveal it. Consider, for example, a person who recently moved to a new city and, apprehensive about driving, decides to ride the city bus each day to work. Riding the bus day after day, the route would be learned through observation, but such learning would only be evident if an incentive was present that required it—say, when it was necessary for the person to drive to work on his or her own. The early findings of latent learning were intriguing and controversial because they challenged the widely held assumption that learning could occur only in the presence of reinforcement. For a classic review of the early latent learning studies, we recommend Tolman (1948), in which the concept of “cognitive maps” was introduced, a term that refers to the mental representation of one’s spatial environment. (Page 177)


What is the difference between these two?

References


Sawyer, R. K. (Ed.). (2005). The Cambridge handbook of the learning
sciences. Cambridge University Press.
Soderstrom, N. C., &amp; Bjork, R. A. (2015). Learning versus
performance: An integrative review. Perspectives on Psychological
Science, 10(2), 176-199.
Implicit Learning


  Implicit learning refers to situations in which complex information is
  acquired effortlessly (without a conscious effort), and the resulting
  knowledge is difficult to express verbally. (Italics mine)


As discussed in the Wikipedia page, the exact definition is controversial, but all the paradigms (verbal reports, forced-choice tests, etc.) listed, the knowledge is gained unintentionally and without awareness. 

Both these criteria relate to the learner's subjective relationship with the acquired knowledge. It says nothing about behavior and reinforcement, which may be readily apparent.

Consider social skills as an example. I may smile, gesture, and make eye-contact appropriately (behavior), and I experience positive social outcomes when I do so (reinforcement). However, I never explicitly set out to learn the number of milliseconds to maintain eye-contact, or what situations warrant a smile. Moreover, if someone offered to pay me to write instructions on how to engage socially, I would have a hard time articulating my knowledge. It is implicit.

Latent Learning


  Latent learning is defined as learning that occurs in the absence of
  any obvious reinforcement or noticeable behavioral changes. (Italics mine)


These criteria relate to the objective behavior and circumstances of the learner. It says nothing about the learner's subjective awareness of the knowledge.

Consider the bus ride example. I may be perfectly aware that I am gaining knowledge of the bus route through observation. But an objective observer would have no way of proving that I have learned the route: I behave the same as if I had not learned it, and I receive no clear reinforcement for doing so. However, if someone offered to pay me to give directions to my work place, I would be able to do so. My knowledge is explicit but hidden.

To sum it up very roughly:

Implicit learning is when the knowledge you gained isn't apparent to you.
Latent learning is when the knowledge you gained isn't apparent to others.