Succession, progression, series, sequence, chain, train, string are comparable when they mean a number of things that follow each other in some order.
Succession implies that the units, whether things or persons, follow each other, typically in order of time or, less often, of place and usually without break or interruption.
Progression (see also PROGRESS 2 ) applies to a succession in which there is movement and flow, and often change, so that a pattern is formed or an advance is indicated. The word is most frequent in mathematics and in music; in the former it denotes a succession of quantities between every two of which there is a particular but an unvarying relation.
In music it denotes a succession of chords which constitute a harmony.
Series applies to a number of things of similar or uniform character that stand in the same relation to each other or achieve the same end; often the term is indistinguishable from succession , but the combined or total effect of the units is rather more stressed than the fact that they follow each other.
Sequence is more restricted in meaning than series and implies a closer causal or logical connection between the things involved (as a numerical or chronological order or a settled recurrence in the same order).
Chain applies to a succession or series which forms a logical or causal sequence.
Train applies to a number of persons, animals, or concrete things or of effects or ideas that follow as attendants or as consequences or sometimes (as in the case of causes) that precede.
String applies to a series or succession so uniform (as in character, size, or quality) that its units are or seem to be strung on a thread; usually there is little implication of chronological, logical, or causal connection.