The purpose of this blog is to share a conversion table, that will give you a rough idea of how scaled scores convert to standardised scores. It is based on distribution of 2018 KS2 scores in reading and maths, taken from national tables. Download the national, local and regional tables (3rd link down) and click on table N2b. The cumulative percentages in table N2b are converted to standardised scores via this lookup table.
The scaled score to standardised score conversion table can be downloaded here.
Please note: this is not definitive; it is a guide. It will also change next year, when 2019 national data is released, but hopefully it will demonstrate that one score does not directly convert into another.