Learn Chinese Grammar: 不管(bùguǎn= don’t care) vs. 无所谓(wú​suǒ​wèi=don’t care):

不管is used when you have confidence (to continue) to do something you think is right, though people said bad things about it.

无所谓 is used when you don't care about something because it's not your business.

Examples:

1. I don't care, I want to eat it.

我(wǒ=I)不管(bù​guǎn=don't care), 我(wǒ=I)要(yào=to want)吃(chī=to eat)。(The speaker has confidence to eat the food; she doesn't care what people said bad things about the food)

2. I don't care, I want to eat now.

我(wǒ=I)无所谓(wú​suǒ​wèi=don't care), 我(wǒ=I)要(yào=to want)吃(chī=to eat)。(The speaker just wants to eat; s/he doesn't care about something that is not her/his business)