Does preferment add sourness to taste of bread?
Your question has a couple layers, so I'll peel those away one at a time!

What causes sourness?
Sourness (the taste, speaking generally) is caused by acidity. The acid (i.e., sourness) in sourdough is created by bacteria (e.g., Lactobacillus spp. which are generally benign and sometimes beneficial, such as inhibiting the growth of some harmful bacteria). More bacteria makes more acid, and more time permits bacteria to make more of the acid, and to multiply. Hence, more time (generally) makes more bacteria and more acid.

Fundamentally, pre-ferment does add sourness to the taste bread, for the aforementioned reason: the extra fermentation time (of the pre-ferment portion of the dough) permits additional time for bacteria to cultivate and produce acid. 

The other part of your question makes a distinction between time: The time duration of pre-fermentation does have an effect on sourness. This is for the same reason: More time permits more acids to be produced by the critters in the dough, which makes the bread more sour. This is supported by your experience: What you're calling "preferment bread" has a longer first (pre-)fermentation stage, and you report it as more sour; in contrast, your "sponge bread" has a shorter pre-fermentation, and you report it as less sour.

I'm using some hedge-words ("generally", "basically", ...) because there's undoubtedly a lot more happening with interactions of starches, acids, enzymes, bacteria, yeast, etc. than I'm discussing here.

I hope it helps! Have fun with your sourdough. Let me know if I've missed the point, or missed part of your question.



More musings below the cut...

Your question (and associated dialog) got me to think about the connotations of terms. This glossary includes some definitions and examples of terms, and how certain types of pre-ferment (e.g., biga, poolish, sponge, pre-ferment) have subtly different connotations. But basically a pre-ferment by any name consists of flour, water, and some source of yeast: either a previous pre-ferment, commercial yeast (e.g., active dry), or some other source (e.g., grape skin).

Other SA questions for additional reading... This question discusses sponges and pre-ferments as pertains to sourdough. This question discusses the soaker as a non-yeast-containing portion of dough, which permits more autolysis ("self-digestion" by enzymes that exist in the flour/grain itself) without necessarily much fermentation.

Other sourness musings...  Even straight dough ("single stage" mixing all ingredients together at one time; i.e., without using any pre-ferment technique) can become (desirably) sour; using less yeast and a correspondingly longer fermentation time will produce a similar (albeit less pronounced) effect. Separately, actual acid could be added directly to the dough, as suggested by this KAF recipe, but that's not necessary or common.