Spiders can spin sticky and non-sticky webbing, and they use only the tips
of their legs to touch the sticky webs.

Spiders produce different kinds of silk for different purposes. A spider
will use dragline silk, which is the strongest kind of silk, to make the
spokes of the web and any part that is intended to bear the weight of the
spider. This silk isn't sticky and the spider can safely move over it to
different parts of the web. The spiral connections of the web are sticky
and are intended to snare prey.