Mobile and desktop scores are assessed differently by PageSpeed. This means that it's possible (and common) to have scores that can be quite different from each other. The concept might seem a bit strange because 'fast' is fast right?
A lot of websites take advantage of modern web development techniques like responsiveness, loading of content only when it is displayed on the screen and disabling/enabling features on mobile vs. desktop. This is a good thing, since the demands of mobile vs. desktop are different.
For example there is no need for high resolution images to download on a small mobile device but they look great on a big desktop display. A popup may be jarring and obscure content on mobile but add a useful feature on desktop.
In this way, smart website coding adapts to the device it is being browsed on. Now it's clear why we can have different PageSpeed mobile and desktop scores: your website behaves differently on mobile and desktop so can be better optimised on one vs. the other.
The Plug in Speed automatic code and image optimizations optimize your shop for both mobile and desktop. Usually it is apps and/or your theme causing a gap between scores. We are happy for no extra charge to highlight why your mobile and desktop speeds are different, just drop us a mail at email@example.com.