Ceremonial vs. Ceremonious

Ceremonial means ‘relating to formal religious or public events’.

Everyone wore formal clothes that suit the ceremonial occasion.
The museum exhibits everything from ceremonial headdresses to modern artwork.

There are some fixed expressions with ceremonial. Examples are: ceremonial garb, ceremonial dress, ceremonial offering and ceremonial dance.

The Sikhs, for example, are known for wearing ceremonial daggers.

Ceremonious

Ceremonious means ‘formally polite’.

The visitors were given a ceremonious reception. (NOT The visitors were given a ceremonial reception.)
After the ceremonious addresses there were some stage performances by the students.
They are rivals but whenever they meet in public, they greet each other with a ceremonious display of friendship.

Fixed expressions with ceremonious: ceremonious welcome, ceremonious address, ceremonious manners, ceremonious speech etc.