If we take the word パーティ, why is テ pronounced as "ti" when in the katakana alphabet it is pronounced "te." Also, why is ィ small? If it was normal sized, wouldn't the pronunciation of the word be the same?
How do you pronounce th in the? Not a t sound and then an h sound, right? You read it as one sound (the voiced dental fricative). Well, it's a similar concept. It's not テ＋イ. It's ティ, with a small ィ, and together they read as "ti". Actually, テイ (regular sized イ) could be "te" with an elongated "e" sound, or it could be "te" + "i". I don't want to get into that, but basically they're not pronounced the same, as you initially suspected.
Regardless, it's not unique to this pair. From Wikipedia,
Small versions of the five vowel kana are sometimes used to represent trailing off sounds (ハァ haa, ネェ nee), but in katakana they are more often used in yōon-like extended digraphs designed to represent phonemes not present in Japanese; examples include チェ (che) in チェンジ chenji ("change"), ファ (fa) in ファミリー famirī ("family") and ウィ (wi) and ディ (di) in ウィキペディア Wikipedia.
I didn't quickly find a duplicate, but here's a somewhat similar question: Why is じどうしゃ (jidoushiya), jidōsha instead?
One of the answers makes reference to the following:
- These additional letters are invented in modern era to describe the sound of foreign languages.
ファ[fa] ティ[ti] ドゥ[du] ウェ[we] フォ[fo]
- ァ, ィ, ゥ, ェ and ォ(small ア[a] イ[i] ウ[u] エ[e] オ[o]) are attached after particular letters.
ヴァ[va] ヴィ[vi] ヴ[vu] ヴェ[ve] ヴォ[vo]
- ヴ is used for [v] sound.
Besides only giving out an explanation, it might be better to state about some Japanese background first.
Some Japanese come from two types of language: Chinese and English (or French, Spanish, etc...). Here by saying "come from", I mean that these words might be "borrowed from" other languages due to some reasons.
For those words that might come from Chinese, they usually have a corresponding kanji besides only hiragana, and the pronunciations are similar to Chinese. For example: 単語（たんご）、日本（にほん）、お茶（おちゃ）、郵便局（ゆうびんきょく）
For those words come from those languages other than Chinese （外来語）, they usually address these in katakana instead of hiragana. They usually don't have a corresponding kanji. Also, due to the lack of alphabets in Japanese, they create some expressions for more correctly address these words. For example: パーティー（party）、フォルダ（folder）
The second one is what you're confusing about. Take the word party as explanation, テshould be pronounced as te originally. However, the alphabet following with テ is in a lowercase (ィ） instead of uppercase（イ）. Thus, in this case, the pronunciation becomes ti（ティ）. If it is written in a uppercase, you should pronounce it as te- （長音 is another story, try to Google yourself if you are not familiar with it.）
How to distinguish when to pronounce it as which one? You can just check the size of the word that follow with it. If it is a lowercase, you should always speak it with the former alphabet. Like the above フォルダ's ォ, so it's not ふおるだ(fuoruda), but ふぉるだ(foruda).
In the case that you speak English, just try to figure out what it's corresponding English word. Then you'll know which one it should be and pronounce it in a Japanese way XD. ( You can cut down a lot of vocabularies you need to memorize by this way.)
By the way, those vocabularies originated from Chinese has two kinds of pronunciations (by 音読み or by 訓読み). The former has a similar pronunciation as it is in Chinese which is my native language so I'm sure it is xddd) It is also another story and you can try to know it in your way for learning Japanese.