One will need to record and graph in some way the physical sound of each example to get a real understanding of how they may differ.

A person can hear some differences that really are not there. That is because of the way one's brain processes the sound. Hearing is a sense that is not always the same from one human to another.

Some "talking dictionaries" may not use the same sounds as other such dictionaries use.

You have divided these words into two groups based on how you hear a particular vowel being pronounced. I have no opinion as to how close the vowels were in the eight words cited; my brain tends to ignore small differences in vowels. However my brain does not ignore many differences in how a consonant is articulated by a sonant (vowel, although others have a different definition). I am sure other people process some sounds differently than I. There is, thankfully, some approximate agreement among most people as to what different sounds are. Not perfect agreement, though.

The bottom lime is that the "usual" pronunciation of any word is never more than "approximately" how it is usually sounded. And, a symbol (letter) used to indicate a sound NEVER indicates more than an approximation of how that symbol is sounded.

The tense–lax distinction

As shown there, the vowel at the end of happy /ˈhæpi/ is what we call the FLEECE vowel. It is a tense vowel, sometimes called the close front unrounded vowel. The vowel in sit /sɪt/ is the corresponding lax vowel, the one that we call the KIT vowel, or sometimes the near-close near-front unrounded vowel.

The difference between your other pair is again that of tense /u/ for the GOOSE vowel versus lax /ʊ/ for the FOOT vowel.

You need to learn to hear the difference between these tense/lax vowel pairs, because hearing the tense–lax distinction is critical to understanding English. Until you can hear it, English will always sound confusing to you.

Here's the chart for all twelve simple vowels (monophthongs) of American English:

Notice how there are contrasting pairs of vowels:

• tense /e/ versus lax /ɛ/, so FACE versus DRESS
• tense /i/ versus lax /ɪ/, so FLEECE versus KIT
• tense /o/ versus lax /ɔ/, so GOAT versus THOUGHT
• tense /u/ versus lax /ʊ/, so GOOSE versus FOOT

In materials for young children, the tense vowels are often called “long” and the lax ones “short”, but this is not a good way to talk about them because vowel length is not phonemic. Plus if you were talking about length, you would have to mention that all three phonemic diphthongs (/aʊ/, /aɪ/ and /ɔɪ/) take longer to say, too.

All that said, the word happy does not always end with a tense vowel in all speakers. In those with happy tensing, it does, but in others it does not. Happy tensing is the more common variety.