VF , the white fungus you saw on your strawberries is most likely
Botrytis cinerea. (same fungus that
DocToxyn made reference too found on some grapes)
When the mycelia (fine filimentous hyphae) become dense enough, the colour is generally more grey. This one is also the major cause
of strawberries rotting in the field during especially wet seasons.
see ---> http://strawberry.ifas.ufl.edu/plantpathfiles/PP-bot-32.JPG
and ---> http://www.extension.umn.edu/yardandgarden/YGLNews/images/strawberrybotrytis-dpp.jpg
Upon ripening, all fruits (including grapes) will become colonized by fungi. That's why they taste the best at peak maturity. Their sugars are fully developed and lots of other tastey biochemicals are present. Strawberries have an especially pleasant fragrance and flavour.

They chose a
fitting Family name
Fragaria. Straw is often used as a mulch on strawberry beds. Which is one etymology in naming the fruit. Reason for the straw? To keep the fruit dry so they don't get moldy.
Quiz time: What is the only fruit that bears its seeds on its outside?
The most common mould in grapes are yeast. Over a 100 species of yeast have been identified, naturally on grapes. That is why old-world cultures who made grape wine, didn't have to add anything to their ripe fruit. Just stomp around on them for awhile and put them up in barrels to ferment.
Today we also inoculate the mash using an isolate of
Saccharomyces cerevisiae. (the genus
Saccharomyces is well chosen, Latin Saccharum = sugar, and this yeast's primary food group

)
iansmith rightly points out the phenotypic differences distinguishing moulds, fungi, yeast and bacteria. Though in mentioning eucaryotes, I thought he would also point out that bacteria are
procaryotic.
I am not convinced of a distinction between "good mold" and "bad mold" that
DocToxyn proposes. For myself and everyone else who happens to be allergic to fungi, all molds are bad molds. I am not familar with allelopathy (chemical inhibition of one species by another) between molds. Generally it is, first come first serve, which ever mold lands there first has first dibs at colonizing the fruit.