I would like to know the difference between the following two sentences:
Ich möchte etwas zu trinken.
Ich möchte etwas trinken.
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Maybe the difference is best explained by translating both sentences:
Ich möchte etwas zu trinken:
I would like something to drink.
The person is stating, that he/she desires the object (or rather: liquid) he/she wants to drink. Note that you could also use etwas zum Trinken.
Ich möchte etwas trinken:
I would like to drink something.
This case emphasises the action of drinking.
Usually, both versions can be used interchangeably, although I would say the first one is more common, especially in situations discussing the act of buying food/drink (the object), like in a restaurant. In contrast, Ich möchte etwas trinken would be a way to tell that you are generally thirsty, and need to drink something (in this case the drinking is more important).