Purchasing a Switch - AC vs DC Current Specifications?
When comparing switching devices for AC and DC use you can specify the acceptable maximum voltages for a common current eg


10A at 230 VAc or 32 VDC


or the acceptable maximum current for a common voltage eg


230V  at 10A AC or 1A DC.


The latter method is usually MUCH less useful. 
 ie almost nobody cares about 230 VDC and few would care about eg 24 VAC.

Specifying current is usually more useful.
 eg for a given system of voltage you usually know if you want to swutch 1A ir 10A or 50A etc.

Re


  Does this current rating apply to both the rated AC and DC voltages?


For a reputable specification the spec applies in a logical manner as stated.
 So if it says 10A, 230 VAC, 32 VDC you can expect the 10A to apply to both.

Occasionally a manufacturer MAY indeed spec both different Voltage and current  eg

12 VDC, 10A   or 230 VAC, 20A

usually because the voltages concerned are standard ones which buyers are liable to be interested in. eg here "car battery" type voltages and mains type voltages.



re


  What is the highest current I could reasonably expect from a DC switch before moving to a relay?


Whatever the manufacturer says.
 You can buy switches of almost any rating.
 10A is common.
 50A is more specialised but not wholly unknown.
 500A would be very very very specialised and you probably want to be wearing a specialised suit when using it (really) BUT they exist.

Realays are not special as of right in switching ability. 
 They exist more because of their remote controllability than because of any ability to switch better.

Switches that are liable to draw an arc that prevents switch "opening" will also have mechanisms to stop this happening.
 This may be as simple as spring loaded flick action which many people will have encountered without realising why they act as they do, through to units with magnetic blowout and arc paths which cause the arc to climb, lengthen and self extinguish. The latter are more the realm of very high capacity breakers but could be used i switches for the brave and foolish if desired.



FWIW there are contactors which may also be used in "switch" mode that are so hazardous that they will usually kill a person in the vicinity if they break rated fault current while people are in the vicinity and which, if they need to be manually operated, require special suits, long poles and lots of luck and still may kill people ... ! 



Glossary: Z ~~= s when the world is upside down.