It marks the relationship, not the politeness of the sentence. You can speak in flat casual Japanese and still say 田中さん, and you can speak in immaculate です・ます and cause offence by choosing くん. The suffix runs on its own channel, and it is read far more closely than the verb endings are.
さん is the default in every direction. Any gender, any age, anyone you are not close to. It also attaches to things that are not people — 本屋さん the bookshop, お巡りさん the police officer. It is usually a safe default when you are unsure how to address someone.
くん and ちゃん both point downward, differently. くん is level-or-below and mostly male: schoolboys, junior colleagues of either gender, classmates. ちゃん is affection — children, close friends, pets, grandparents — and because it claims closeness, using it on someone who has not granted it is a small trespass rather than a compliment.
様 is not extra-polite さん. It is the formal ancestor the everyday word wore down from, and it kept the distance. お客様 is normal, an envelope takes 様, and calling a colleague 田中様 to their face is either ceremony or sarcasm — there is no ordinary use in between.
A title takes the slot. 先生, 社長, 部長 already carry the honour, so they replace さん rather than joining it. Both errors are audible: 山田先生さん doubles it, and 山田さん to someone whose title you know quietly takes it away.
Never attach one to your own name. An honorific is something you give, not something you wear, so 田中さんです about yourself is wrong — it is 田中です, or 田中と申します. Small children genuinely do refer to themselves as 〜ちゃん, which is exactly why it lands the way it does when an adult does it.
