Sequence data vs time series data
Sequential Data is any kind of data where the order matters as you said. So we can assume that time series is a kind of sequential data, because the order matters. 
A time series is a sequence taken at successive equally spaced points in time and it is not the only case of sequential data. In the latter the order is defined by the dimension of time. There are other cases of sequential data as data from text documents, where you can take into account the order of the terms or biological data (DNA sequence etc.). 
The fact that you have sequential data is important for two reasons. First, you can into account for the representation of the data and also you can take it into account for the data modeling (e.g. Conditional Random Fields, Hidden Markov Models for text or genes and ARIMA Models for time series problems).