As I haven't studied the schools of singing and their language sufficiently to give a definitive answer, I can only interpret the informations vocal teachers give according to my experience.
A laryngeal tilt is a specific configuration at the larynx, which is important for hitting high notes without strain, while maintaining a rather full sounding voice and smooth control over the intensity.
I think when they want you to sing "down to the higher notes", the intention is to use that very mental idea to find and utilize a sensation corresponding to a skillful coordination. The idea itself can help you more to find that coordination than understanding what is supposed to happen technically. I think it addresses the intuitive approach the vast majority of people have towards high notes: They use the wrong muscles and this results in a lot of effort and strain. As a result, they think of high notes as something to reach for. By reverting that image, teachers encourage them to let go of this counter-productive contortion. So it's mostly about what not to do, but this in turn helps you to develop the right engagement, which includes, but is not limited to a laryngeal tilt.
Vowel modifications are obviously a quite fuzzy concept with many different meanings, aspects and subtleties and I don't want to go too far into that rabbit hole.
I think vowel modifications have three aspects relevant for your question:
- The tongue is a big mass of muscles important for both vowel formation and resonance, and what it does is connected to what happens at the level of the larynx. As a result, how we shape our vowels encourages different things to happen at the level of the larynx and in the resonator. Good pharyngeal resonance in turn supports the vocal folds in their vibrations. Therefore, changing the tonal quality which we perceive as part of the vowel can help us to find the coordination and tone depending on what we need in any particular situation (which also might include a laryngeal tilt). Over time, we learn to coordinate the larynx much more independently of the vowel we are singing, and vowel modifications in this sense become obsolete, or at least can be kept much more subtle.
- Essentially, vowels can be defined in terms of the frequencies of specific resonances called formants, the most significant of which in this respect are the lowest two. The closer the frequency of a harmonic in your voice lies to a formant, the louder the harmonic will be. As already hinted above, such resonances are important for a nice timbre, but also to maintain focal fold vibrations at a higher pitch. When the pitch raises, the harmonics shift across the formant landscape and get more and more dispersed. As a result, keeping the vowels (formants) exactly the same as you ascend will lead to more and more significant losses of resonance, and pretty easily, the old strain can kick in again. You can prevent this by adjusting the vowel, so that the first two formants lie close to harmonics. Well, you can hit harmonics exactly with the second formant to create those colorful clear mids and use vowels to sing harmonies on top of your melody...
- Sometimes we need to modify our vowels to return to our healthy range of motion. Evolving singers tend to misuse vowel modifications unconsciously. As they try to follow the second or third harmonic with the first formant, they push the vowel across its natural limits, which inevitably induces strain adding to the perceived "ceiling" at some point in their range. Ironically, the remedy is called a vowel modification, although in fact, it's actually a relaxation of a habitual modification that's already happening. This is probably because when we do not modify the vowel as we ascend, it seems to get darker. Conversely, in order to maintain the same relation between the formants and harmonics, you have to modify it.
To wrap it up, laryngeal tilt and vowel modifications are different concepts and no alternatives to each other. You might focus on one or the other, but eventually both should need to happen to some extent (no matter what you do, you're always modifying your vowels according to some definition).
