I actually find it hard to pin down psychedelia as a musical style. You sort of know it when you hear it for the more outlandish examples. But given songs as disparate as Eight Miles High and Tomorrow Never Knows get classified as such it's hard to find the common elements.
As for progs relation to psych, it seems like there should be some link or development but I'll leave that to more experienced prog ears.
Hey Moog, psych is easy to identify really, it came just before the late 60's hippy period and continued through it, the two tracks you mentioned are disparate yes but the general genre is in focus, the drug references (especially LSD) and the general 'trippy' feel of the recordings, maybe monks chanting or a Celeste ......Lucy In The Sky was a classic psych tracks of course, Strawberry Fields, you could say anything thats 'Far Out'
Lots of late 60's bands jumped on the psych bandwagon, Piper At The Gates Of Dawn was like a reference for psych and Syd Barrett one of its founders (maybe its CEO)
Prog really started in England in 1969, the first full blown album was definitely King Crimsons In The Court Of The Crimson King, which has been identified as THE first album to include all the hallmarks of progressive rock and its form. Which are;
Progressive rock songs either avoid common popular music song structures of verse-chorus-bridge, or blur the formal distinctions by extending sections or inserting musical interludes, often with exaggerated dynamics to heighten contrast between sections. Classical forms are often inserted or substituted, sometimes yielding entire suites, building on the traditional medleys of earlier rock bands. Progressive rock songs also often have extended instrumental passages, marrying the classical solo tradition with the improvisational traditions of jazz and psychedelic rock. All of these tend to add length to progressive rock songs, which may last longer than twenty minutes.
Timbre (instrumentation and tone color): Early progressive rock groups expanded the timbral palette of the then-traditional rock instrumentation of guitar, organ, bass, and drums by adding instruments more typical of jazz or folk music, such as flute, saxophone and violin, and more often than not used electronic keyboards, synthesizers, and electronic effects. Some instruments – most notably the Moog synthesizer and the Mellotron – have become closely associated with the genre.
Rhythm: Drawing on their classical, jazz, folk and experimental influences, progressive rock artists are more likely to explore time signatures other than 4/4 and tempo changes. Progressive rock generally tends to be freer in its rhythmic approach than other forms of rock music. The approach taken varies, depending on the band, but may range from regular beats to irregular or complex Time Signatures.
Melody and Harmony: In prog rock, the blues inflections of mainstream rock are often supplanted by jazz and classical influences. Melodies are more likely to be modal than based on the pentatonic scale, and are more likely to comprise longer, developing passages than short, catchy ones. Chords and chord progressions may be augmented with 6ths, 7ths, 9ths, and compound intervals; and the I-IV-V progression is much less common. Allusions to, or even direct quotes from, well-known classical themes are common. Some bands have used atonal or dissonant harmonies, and a few have even worked with rudimentary serialism.
Texture and imagery: Ambient soundscapes and theatrical elements may be used to describe scenes, events or other aspects of the concept. For example, Leitmotif is used to represent the various characters in Genesis' "Harold the Barrel" and "Robbery, Assault and Battery." More literally, the sounds of clocks and cash registers are used to represent time and money in Pink Floyd's The Dark Side of the Moon.
Album art and packaging is often an important part of the artistic concept.
This trend can be seen to have begun with The Beatles' Sgt. Pepper's Lonely Hearts Club Band and played a major part in the marketing of progressive rock. Some bands became as well known for the art direction of their albums as for their sound, with the "look" integrated into the band's overall musical identity. This led to fame for particular artists and design studios, most notably Roger Dean for his work with Yes, and Hipgnosis for their work with Pink Floyd and several other progressive rock groups.