"Have to" and "have got to" both mean "must". When saying "have got to", it's natural to abbreviate 'have' (ex. "I've got to..." or "John's got to...") Some English speakers just say "got to" without saying "have". This is slang. When speaking quickly, "got to" often comes out as "gotta". This is usually unintentional, and just the result of speaking quickly. "Gotta" is never written, except when quoting someone who said it.

When you say "I have" it usually implies ownership. When you say "I got" it usually implies you received something.

It is better to use "have to" in a sentence. The word "gotta" is slang.

Many thanks :)

The former is standard; the latter is colloquial.