There might be a subtle difference between the two, but it isn't enough that even a native speaker would know the difference offhand. They both mean elaborate displays and ceremony.

The meanings overlap a lot. I never thought about it until you asked. "Pomp and pageantry" is a common colocation. A "pageant" can literally be a kind of show or performance--a big, elaborate event, usually showing with an historical or religious theme. So "pageant" emphasizes size and visual spectacle, hundreds of people, costumes, grandeur. "Pomp" emphasizes something solemn, dignified, or important. If someone is talking about the coronation of Queen Elizabeth II, and they use the word "pomp," I think of the quiet moment when the archbishop actually puts the crown on the Queen's head. If they use the word "pageantry," I think of the outdoor spectacle of the Queen riding in a gold coach with people in uniforms marching and thousands of people lining the street and cheering

The words "pomp" and "pompous" have the same root. When people hear "pomp", they are likely to associate it in their minds with "pompous", which has a feeling of boastfulness. "Pageantry" does not carry the burden of this hidden meaning.

Pomp and pageantry are both associated with grandeur and ceremonial display, but there are some subtle differences between the two terms. Pomp generally refers to the impressive display of ceremony, dignity, and grandeur, often with a focus on the use of elaborate costumes, decorations, and musical accompaniment. It can be associated with official ceremonies, such as state occasions, religious events, or academic ceremonies. Pageantry, on the other hand, is a broader term that can refer to any kind of elaborate display, including theatrical performances, parades, and festivals. It can also be associated with historical reenactments, beauty contests, and other forms of public entertainment that involve elaborate costumes, choreography, and music. Overall, while both pomp and pageantry involve impressive displays of ceremonial grandeur, pomp tends to be more closely associated with official ceremonies and formal events, while pageantry can encompass a wider variety of events and activities.