It was getting lighter outside so I continued reading without a torch. (there was no break in action, i.e. reading)

It was getting lighter outside so I continued to read without a torch. (there was no break in the action (i.e. reading) mentioned, but there could have been one)

Dann bedeutet also die to-Form, dass möglicherweise eine Unterbrechung stattgefunden hat. OK. Vielen Dank, das hilft mir!

Zum besseren Verständnis (und weils sinngemäß das gleiche ist):

I stopped smoking. (Ich hörte mit dem Rauchen auf.)

I stopped to smoke. (Ich hielt an, um zu rauchen.)

Wie denn nun?
Sniffer redet von einer möglichen Handlungspause, Boschhammer (wie übrigens die Eingangsfrage von streifenhörnchen) von dem Unterschied zwischen fortgeführter Handlung (-ing) und Handlungsziel (to ...).

Könnte das mal ein Muttersprachler klären?

I've thought about this, and I really think there's no difference. I disagree with sniffer and think a break can be implied even with the -ing form. For example:

I continued smoking all throughout the 60's.

I continued to smoke all throughout the 60's.

Obviously the speaker did not smoke constantly through the entire decade. To me, these sentences mean exactly the same thing.

Stopping, as Borschhammer points out, is another matter.