in easy way we can say GOTTA is an informal, you can use it will talking (informally). HAVE TO & MUST are the formal forms but the difference is HAVE TO = you will do the action 70% to 90% MUST = you will do the action 99%. This shows stronger intention.

Must = have to = have got to 'Have to' and 'have got to' are just casual versions of 'must'. When people talk quickly, 'got to' sometimes becomes 'got tA' accidentally. This is never written, except when quoting someone who said it (where it is spelled 'gotta'). Ex. I must eat something. I have to eat something (casual) = I've got to eat something (casual) = I got to eat something (slang, because the 'have' is missing)