Difference between Time series clustering and Time series Segmentation
Actually there is no fixed terminology and these two terms sometimes used in the same meaning and sometimes different. I would suggest following the terminology bellow for yourself, then you can differentiate methods according to this:


Time-Series Segmentation means partitioning an individual time series to similar segments i.e. clustering within an individual time-series (e.g. i have a video in which someone is reading a book for a while, then starts walking and then starts cycling. now I want to segment these three actions).


Suggestion: State-Space reconstruction, moving Autocorrelation, moving DTW, Fourier Analysis, Visibility Graphs or any other method which can measure the similarity of a time-series with itself. 


Time-Series Clustering (or this) means finding similar time-series within a dataset of time-series (e.g. i have 10 brain signals, 5 from healthy subjects 5 from patients without knowing who is patient and who is healthy. Now I want to cluster this dataset into two clusters)


Suggestion: Build a similarity matrix between time-series using e.g. DTW and then apply Spectral Clustering (just improvised. If you search literature there should be more mature solutions)

Hope it helped :)