What's the difference between image and likeness?
As Nihil Sine Deo discussed, image and likeness are similar but carry slightly different connotations:
An Image carries with it the idea of the representative or stand-in function of the one so designated and relates more to one's role than to one's appearance. For an image or idol, it was more important what it represented than what it looked like.
Likeness relates more to the visual appearance.
The immediate context of image and likeness found in Genesis 1:26 relates to man's rule over the creatures in the earth, sky, and sea.
Therefore, Man's designated role in creation is to function as God's images - God's ruling representatives on earth.
To the extent that we obediently and faithfully represent God, when we are looked upon, God's likeness - God's wise and righteous rule in our lives - can be seen and should be apparent to all.
Bonus answer to a question you didn't ask:
This is what was meant by Jesus, the image of God, when he said, "The one having seen Me has seen the Father." When we look upon Jesus, God's ultimate obedient and faithful representative, we see the likeness of the Father in the son's lived wisdom and righteousness and love.
Bonus answer to a second question you'd didn't ask:
Understanding the image of God as a role or office designated to the created class of human beings helps us to resolve issues presented by viewing the image of God as defined by a particular set of attributes like intelligence and decision making.
What about humans who aren't particularly intelligent or are not able to make decisions?
(like babies or the mentally impaired)
Can they be considered to not be God's images since they don't have these attributes?
If they lack these attributes are they no longer protected by God's command to Noah that, “Whoever sheds the blood of man, by man shall his blood be shed, for God made man in his own image" (Gen 9:6)?
Are we free to shed the blood of sub-images who lack these attributes?
Well, of course not. The entire human class has been created in the office of the image of God. It doesn't matter how broken we are or how good of a job we do. We are God's images as a matter of creation, and for that reason alone we all deserve dignity.