Timid
1. Shrinking from dangerous or difficult circumstances; hesitant or fearful.
2. Shrinking from public attention; shy.
Cowardice
Lack of courage in the face of danger, pain, difficulty or opposition.
Those are the dictionary definitions. In everyday usage, timid and shy are synonyms. A timid person is one who does not usually initiate conversations, actions etc. There is no negative connotation attached to the word.
Although a coward is a timid person, it goes farther than that. The word has a dishonorable connotation. It connotes one who shirks his duty, one who is afraid to do what is required of him. While it most often applies to one who avoids his responsibility in the face of danger, as a soldier in battle, for instance, it can also apply to more subtle situations. There are those in my country today who feel there is something cowardly about those who willingly sacrifice young Americans in unnecessary wars while they themselves remain far from any danger. It is precisely the dishonorable nature of their behavior that earns them the epithet of coward, at least in the eyes of those who distinguish between defense and offense.
A poltroon is a base coward but that word is archaic.
A recreant is one who is “unfaithful or disloyal to belief, promise or cause.’’ One comes across it, mainly in writing, in that sense – false, unfaithful.