They do all mean much the same thing, but are used in different contexts.
'Change' is the most general : 'the weather has changed; it was sunny this morning, but now it is cloudy'.
'He has changed recently; he used to be so friendly, but now you can't speak to him'.
'I'm going home to change my clothes'
In some cases, you can substitute 'turned in to' for 'changed' :
'Since his father died, he has turned in to a recluse, he doesn't talk to anybody'.
'If you leave this out in the sun, the soft surface will turn in to a hard layer'
You have to 'turn in to' something [which is stated].
'Switch' usually implies a deliberate act of changing something : 'I am going to switch my telephone network to ABC'
'Since I switched to the early shift [duty], I have more time in the evening.'
It can also mean 'to turn' something on or off : 'Can you switch the light on please'.
'Is the machine switched off ?'
'Convert' has rather specific contexts of usage : currency is converted from, for example, dollars to another country's money; a measurement on one scale may be converted to its equivalent on another e.g. 5 miles distance may be converted to 8 km., etc.
People can be 'converted' to a cause, or a religion : 'If you marry her, you will have to convert to Islam'
'I've been converted to the benefits of regular exercise'.
Buildings, or parts of buildings, can be converted to fulfil another function : a 'loft conversion' creates a new bedroom from the space in the roof of a house.
A 'catalytic converter' cleans the exhaust emissions of a motor vehicle to make them less harmful.
No doubt there are many more situations in which things are converted from something to something else.