An economic slowdown means that the rate of growth of an economy (i.e. how much the economy is worth: creation of wealth) starts to drop. For instance, if for the last few months the economy was growing at a rate of 3.5% and next month it grew at only 1.5%, you would say the economy had slowed down quite significantly.
A recession means that the economy actually shrinks, i.e the volume of money in the system decreases. This would be manifested in the closure of businesses etc, i.e. institutions that cause spending.
I'm no economist but I think this is about right.