I find it difficult to make
dolce (sweetly) and
cantabile (singing/songlike) sound different when I'm playing the piano.
How should my technique differ from one to the other?
I like to think about dolce as applied to character, and cantabile as applied to articulation.
The dolce instruction gives you an idea more linked to the character, to a feeling that your playing might suggest. This reflects directly into the dynamics of the piece you are playing, although not strictly as bound to the "speed vs. strength" matter as it regards more to delicacy, "warmth" and other timbral qualities (therefore more abstract). You should take such an instruction as a stimulus to your general feeling when playing, trying to strike each note with adequate intensity to achieve a soft, smooth tone -- and, for effect, allow for more sensible dynamic variations through more intense sections.
As for the cantabile, this is especially effective for passages where notes are bound together by short melodic intervals. Note also that this is specifically linked to melody, whereas dolce can affect the overall playing. When playing cantabile, one should note immediately the easy melodic flow, the legato vs. staccato factor, the conduction of the intensity as depending on the direction of the movement (higher pitches should imply more effort, more air, and therefore more intensity when executed by a singer; leaps should call for a more poignant attack, and so on). Long story short, you should really try to emulate the nuances that the human voice could give to that melody, paying special attention to the articulation between notes, phrases and gestures.