Hi Vada,
Great questions! I’m actually going to answer the second of these three questions first.
The term vowel team is used to describe when two or more letters "work together as a team" to spell one vowel phoneme (sound). These vowels might be considered short (as in the /ĕ/ phoneme in ‘head’), long (as in the /ē/ phoneme in ‘beak’), or diphthongs (as in the /oi/ phoneme in ‘moist’). Note that the same vowel sound may or may not be spelled with a vowel team in any given word. For example, the /ē/ sound is spelled with the singular letter <e> in ‘he,’ but with the vowel team <ee> in ‘beet’. While vowel teams always spell vowel sounds, they may use letters that are typically consonants, such as the vowel team <igh> representing the /ī/ phoneme in ‘light.’
Diphthong, however, is a term we use to describe vowel sounds, regardless of how they are spelled. Diphthongs are produced by gliding from one mouth position to another. Watch in a mirror as you say the /ou/ sound (as in 'couch'). Even as you say this single phoneme in isolation, you’ll notice your lips moving. Try this same experiment with the diphthong /oi/.
When working with students, it’s helpful to explicitly point out that both /oi/ and /ou/ are each considered one singular sound. Students might otherwise feel the significant mouth movements needed to make these phonemes and think that each consists of two sounds, impacting their ability to segment words into sounds and subsequently spell such words.
The term diphthong might become a little confusing as you begin to dig deeper, however, depending on your sources of reading and learning materials. Although teachers generally think of English phonology as having the two diphthong phonemes referenced above (/oi/ and /ou/), linguists and SLPs attribute diphthongization to other vowels as well, such as the long /ī/ sound. To notice this subtler diphthong, first contrast the example with a non-diphthong by holding out the /ŏ/ sound (as in 'hot') for several seconds, as if a doctor were looking in your mouth. Pay careful attention to how you can do so with no movement in your mouth whatsoever, and no changes to the sound you are producing. You already know from the mirror experiments that you can’t really hold out the /oi/ or /ou/ sounds in the same way. At some point, you will need to change the shape of your mouth, and subsequently how the phoneme sounds, in order for it to be recognizable as the intended phoneme. Other vowels also require movement shifting as well, making them diphthongs as well. Try to hold the /ī/ sound for several seconds. You’ll notice that you need to shift the shape of your mouth to accommodate pronouncing this sound.
Many professional development and educator prep programs don’t include the level of nuance to explain all of the vowels that are actually diphthongs (or other classifications for vowels such as tense and lax), because it’s generally understood and agreed upon that teachers don’t need this level of specificity in their linguistic backgrounds in order to effectively teach children how to read and spell. In the same vein, I personally don’t generally teach terms such as diphthong to children, as there isn’t any research to suggest that knowing descriptive phonetics terminology is necessary or helpful for children learning how to read and spell. Instead, you can help students become aware of vowel characteristics using student-friendly terms. For example, after modeling a sound such as /ou/ and asking students to repeat it, you might say, “This sound is different from a lot of our other vowels, because I can really feel my mouth move while I’m saying this sound! /ou/ You can even see my mouth move, can’t you? /ou/ You try!... Even though our mouth moves while we say /ou/, we consider it one sound. Let’s practice it with some words. Listen to this word: cow. How many sounds are in cow? That’s right, there are 2 sounds in cow, /k/ and /ou/.”
We covered a lot here, so to summarize: vowel team describes how we sometimes spell some vowels. Diphthong refers to the properties of some vowel sounds that require mouth movement to produce. While diphthongs are often spelled with vowel teams, they are not always. And while some vowel teams represent diphthongs, this again is not always the case. Lastly, while the term ‘vowel team’ might be helpful for beginning readers to understand that one vowel sound can be spelled with more than one letter (similar to a consonant digraph like <sh>), the term ‘diphthong’ is unlikely to be as helpful. Simply pointing out that these are one singular sound despite feeling our mouths move should be sufficient.
Thanks for letting me geek out a bit with my background as an SLP; I hope this helped!