A crank is a type of lever attached to a shaft, drum, wheel, etc, to rotate the shaft when force is applied.
A ratchet is a mechanism with (usually) a toothed wheel and a hinged item called a 'pawl' that engages in the toothed wheel. It can be added to a crank. The important feature and use of a ratchet is that it allows the shaft to be turned in one direction only. If the shaft tries to turn backwards, the pawl engages in a tooth of the wheel, and stops it. This might be a useful safety or convenience feature in many situations.
In figurative speech, we can say that we 'crank something up (or down)' when we mean to increase (or decrease) that thing, for example the speed of working, amount of work done, etc. Probably because the action requires effort, we mostly crank things up, not down.
Likewise, we can say we ratchet something up (usually) when we mean that we make it increase in some way, with no possibility of it decreasing, coming down, or slipping back. For example, we could ratchet up the pressure on a person to do something (e.g. make a decision, change their mind, do something we want, etc). We would only change the thing discussed in one direction, and would not intend to relax the force.
A problem may be that many people don't understand very much about even simple machines like these, and may use the terms interchangeably.