Like, it seems: 〜みたい

〜みたい is the casual version of 〜ようだ. It has the same two meanings: “it seems that” (a guess) and “like” (resemblance). It attaches directly to nouns and な-adjectives, without の or な.

• かぜを ひいた みたい。かぜを ひいた みたい。I think I've caught a cold.
• 田中さん、今日は 休みみたいだよ。たなかさん、きょうは やすみみたいだよ。Looks like Mr Tanaka is off today.
• あの 人、子どもみたいだね。あの ひと、こどもみたいだね。He's like a child, that one.
• この ケーキ、本物の 花みたい！この ケーキ、ほんものの はなみたい！This cake looks like a real flower!

みたい is ようだ in its everyday version. You hear it everywhere among friends, in the family, in TV dramas. The two meanings are the same: “it seems that” (I'm deducing it from what I see) and “like” (it resembles…).

• 外、雨が 降って いる みたい。そと、あめが ふって いる みたい。Looks like it's raining outside.
• この 店、もう 閉まった みたいだね。この みせ、もう しまった みたいだね。Looks like the shop's already closed.

The big difference from ようだ: before みたい, nouns and な-adjectives take neither の nor な. Otherwise, みたい behaves like a な-adjective: みたいな + noun, みたいに + verb.

• この 部屋、ホテルみたいに きれいだね。この へや、ホテルみたいに きれいだね。This room is as clean as a hotel.
• 田中さんみたいな 人に なりたい。たなかさんみたいな ひとに なりたい。I want to become someone like Mr Tanaka.

みたい is perfectly correct, but it sounds spoken. With です, it works fine in polite conversation (みたいです). In a serious written text, a report or a formal letter, however, you write ようだ.

• すみません、電車が 遅れて いる みたいです。すみません、でんしゃが おくれて いる みたいです。Excuse me, it looks like the train is delayed.
• 電車が 遅れて いる ようです。でんしゃが おくれて いる ようです。It appears the train is delayed. (more careful)

Same sound, nothing in common. 見たい is the verb 見る + たい: “to want to see”. みたい (always in hiragana) is an ending: “it seems, like”. To tell which is which, look at what comes before: a plain-form verb or a noun → みたい; an object with を → 見たい.

• あの 映画が 見たい。あの えいがが みたい。I want to see that film.
• あの 人、映画の 中の 人みたい。あの ひと、えいがの なかの ひとみたい。That person looks like someone out of a film.