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Models with stochastic trends i.e., structural time series models are useful in some instances. Firstly, it may be hard to identify multiple structural breaks in the deterministic trend when the sample size is small. Secondly, implementing endogenous multiple structural break tests is a demanding exercise. Therefore, using stochastic trends sometimes instead of deterministic trends makes sense.

However, is there a clear distinction between a stochastic trend and a deterministic trend by when to use it ect.?

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    $\begingroup$ This answer seems to cover some of your question. $\endgroup$
    – Glen_b
    Commented Jun 20, 2013 at 0:04

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