As auxiliary verbs, we use these pronunciations almost all the time. In writing, we use the full forms: "going to" and "got to." "Gotta" can also be "got a" -- but again, only in the spoken language, or maybe SMS between junior high school kids.

gotta is got to, and gonna is going to. tener que is got to and ir a plus infinitivo is going to

Gonna = voy a ..va a .. vamos a..van a.. vas a .. Gotta = tengo que.. tienes que.. (y todo eso ) (:

Entiéndalos cuando los veas. No los usen. Son corto para los frases "going to" y "got to." Se ocurren en habla, cuando la gente habla en una manera rápido, relajado, o descuidadamente. En la impresión, muestran el sonido del pronunciación incorrecto. No las son palabras. No vas a encontrarlos en el diccionario. Autores frecuentemente usan esta clase de deletreo en dialogo. Por ejemplo, Mark Twain, "Huckleberry Finn:" “Doan’ hurt me—don’t! I hain’t ever done no harm to a ghos’. I alwuz liked dead people, en done all I could for ‘em. You go en git in de river agin, whah you b’longs, en doan’ do nuffn to Ole Jim, ‘at ‘uz awluz yo’ fren’.” "Doan," "alwuz," "en," "git," "de," "nuffn," "fren'" no son palabras en el diccionario, estan los sonidos de la habla de Jim. Algunas veces "gonna" y "gotta" se vean en mensajes de texto, y otros como "l8r" en lugar de "later" o "k" en lugar de "OK." Algunas veces se vean en títulos de canciones y letras de canciones. Algunas veces se vean en subtítulos de las películas.

Gonna is a contraction used for going to. But only when used as auxiliary verb. If you use it as a verb, you always use the complete word both in writing and orally. I'm gonna vote tomorrow. I am going to the voting booth very early. Gotta, which is a contraction of got to, follows pretty much the rule as gonna. Only use it as an auxiliary verb, never a stand alone verb. He said, "You've gotta vote tomorrow". But when we got to the voting booth, the line was too long. Both gotta and gonna are usually only used in speaking. They are only used in writing when they are quoted, such as in a book, story or newspaper article, in very informal letters between friends or family, or if a kidnapper is forcing you to write a ransom letter at gunpoint (that's what it would take to get me to write like that). A quick note about "got a". Although, when spoken it sounds a lot like gotta, in writing, even the most informal writing, it is almost never spelled gotta. And if it is, it is usually a stylistic choice by the writer to ensure the reader pronounces it informally. Si necesitas, también lo puedo explicar en español.