At my table I have ruled that 'to use as a spellcasting focus' does not imply 'to play'; since the sorcerer can simply point a wand, it seems like an undue burden that the bard should have to use both hands and/or his mouth to cast the same spell. We've decided that the bard merely holds his instrument, which perhaps emits a few notes on its own as the spell is cast.
However, I noticed that in questions like 'What counts as a bardic focus?' and 'Can a pan flute be played one-handed?', the assumption that bards have to play their spellcasting focus goes unchallenged, so I thought it warranted its own question: Does a bard have to play a musical instrument when using it as a spellcasting focus?
I've reproduced what I think are the relevant rules below. The language appears identical to that of the spellcasting foci of other classes.
PHB p. 53
You can use a musical instrument (found in chapter 5) as a spellcasting focus for your bard spells.
PHB p. 154 (the chapter 5 text)
...A bard can use a musical instrument as a spellcasting focus, as described in chapter 10...
PHB p. 203 (the chapter 10 text)
Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell... A spellcaster must have a hand free to access these components, but it can be the same hand that he or she uses to perform somatic components.
The only distinction I saw is that musical instruments are considered 'tools' while all the other spellcasting foci are 'adventuring gear'. Also the chapter 5 text appears between two statements about proficiency, which sort of implies that the bard must be proficient with their focus (which to me is less of a problem).