What's the difference between movetime and the Slow Mover option? When I tell the engine to find the best move with 

go movetime 1 depth 1


I expect it allows itself to take up to about 1 ms to make it's move. But what's the difference between that and the Slow Mover option: 

option name Slow Mover type spin default 84 min 10 max 1000


Looking at this post from 2008 it seems like perhaps Slow Mover was implemented before the movetime option?
When you pass movetime to an engine via UCI, you're telling it to override any time management algorithms it might have, and to instead spend exactly x milliseconds analysing the position. 

When playing games, the UCI movetime parameter typically isn't specified. Instead, the engine is told how much time each player has left on their clock (and the increment, if any). This allows the engine to decide how much time to use with its own time management.

The Slow Mover option is used to tell the engine how you would like it to manage time. It only means something in a game situation (i.e. when movetime isn't specified). Higher values will tell the engine, broadly, to use "more time", but it does not control the exact amount of time that is used.