Q:

How does abduction differ from inductive reasoning?

Consider this statement:

Abductive reasoning typically begins with an incomplete set of
  observations and proceeds to the likeliest possible explanation for
  the set.

But couldn't the same be said about inductive reasoning? Someone finds a penny in a jar. Then they find a second and a third penny, so they conclude that all the coins in the jar are pennies.

Three pennies constitute an incomplete set, so how is that different from abduction?
What example of abduction would complement the following two deduction/induction sets?
DEDUCTION #1: All mammals have vertebrae; llamas are mammals. Therefore, llamas have vertebrae.
INDUCTION #1: The first three bones found in Cave X were vertebrae. Therefore, the other bones may represent mammals.

ABDUCTION #1: ???

DEDUCTION #2: All planets orbit stars. Earth is a planet. Therefore, Earth orbits a star.
INDUCTION #2: Astronomers have pronounced Object X a planet. The nearby Object Z is also a planet. Therefore, Object X and Object Z probably orbit the nearest star.

ABDUCTION #2: ???

A:

You are not alone in finding difficulty in distinguishing abductive from inductive reasoning. It doesn't help that 'abductive' inference is a relatively new term in philosophy - historically much more recent than 'deductive' or 'inductive' - or that there is no canonical statement of it. 
Will you bear with me a bit while I try out some contrasts ? 
In a deductively valid argument the conclusion cannot be false if the premises are true. Well, we know abductive inference is nothing like that. 
In an inductively strong argument, the conclusion is merely unlikely to be false if the premises are true. 
So what ground is left for abductive inference ? It's really an intelligent guess. It's not just a guess, it's an intelligent guess. Peerhaps this can be illustrated by an example from CS Peirce (wjo some say and others deny originated the notion of abductive inference). He was btw writing long ago : 
THE FOUR HORSEMEN EXAMPLE

I once landed at a seaport in a Turkish province; and, as I was walking up to 
    the house which I was to visitr, I met a man upon horseback, surrounded by 
    four horsemen holding a canopy over his head. AS the governor of the province 
    was the only personage I could think of who would be so greatly honored, I 
    inferred that this was he. This was a hypothesis.

Maybe one difference between induction and abduction is that induction often relies on regularities or lawlike correlations. It is an inductive inference that if I smoke 60 cigarettes a day for twenty years, I will get lung cancer. It doesn't deductively follow that I will but there's an uncomfortably high probability. 
Or : what is the likelihood that if I earn more than $100,000 a year I will be audited by the tax authorities ? Regularly about 5% of people on this income scale are audited, so the probability is quite low. (Figures invented.) 
In the case of Peirce's abductive inference about the governor, nothing like these regularities or lawlike correlations are in play. Yet he made an intelligent guess. On this occasion in the light of Peirce's knowledge of social customs, it was the inference to the best explanation that the person was the governor. 
There is an academic squabble over whether abductive inference and inference to the best explanation are the same thing. I assume they are. Those who disagree can make their case. 
References : 
The Four Horseman example and the phrase, 'intelligent guess', are taken from Douglas Walton, 'Abductive Reasoning', Tuscaloosa : University of Alabama Press, 2004, 5-6. Walton also discusses the abduction/ inference to the best explanation : 6. 

A:

Induction is about the probability of something. Abduction is an assumption as to what is the most likely answer - it's a judgement call.
ABDUCTION #1: The bones of 3 llamas were found in Cave X; therefore the vertebrae found in Cave X are likely from a llama. (since we already found 3 llamas, it's likely that the bones found are also llamas)
ABDUCTION #2: Object A orbits around the Earth. Object A is probably a moon. (it could be a satellite, but judging by the conversation about planets and stars, it makes more sense to assume it's a moon).
Deduction is something that always appears to be so. Induction is something that sometimes appears to be so. Abduction is the best assumption about something. 
So for instance: 
Deduction: Rain is water. Water makes things wet. Therefore, when it rains, the grass becomes wet.
Induction: It's 90 % chance of showers tomorrow afternoon: therefore, it will probably rain tomorrow afternoon and the grass will be wet. 
Abduction: The grass is wet in the afternoon; it probably rained. vs. The grass is wet in the morning, it is probably wet because of dew, not rain. (the best explanation for/an intelligent explanation).

