SST can mean a lot of different things and HST can easily be modified to focus more on strength. Like tim said, lower volume, staying in a lower rep range... I usually work in the 5 RM or lower range and it's good for strength. DC, for instance, is one variant of HST that follows all the principles but has more of a strength focus. DC worked great for me though I ended up getting an injury. There aren't going to be a whole lot of differences because a good strength specific routine, in my opinion, is still going to follow the important parts of HST - chronic vs acute stimuli, progressive load, mechanical load vs fatigue as a factor behind progress... basically you are going to want to workout with a decent frequency still, focus on increasing the load you are using on the bar, etc.
If you are looking to layout a strength cycle, we can help you with it.