A cathedral is "the Bishop's church" -- the chief church of a diocese. The
word is derived from the Greek kathedra through the Latin
cathedra, meaning throne or seat, which is the symbol of authority.
A basilica is a church with important canonical status and privileges, usually
due to its history. There are two types of basilicas:
Major basilicas have a special "holy door" and a papal throne and an altar
at which none may say Mass except by the pope's permission. They are also
called "patriarchial basilicas" and are associated with the great patriarchates
of the world, for ex.:
St. John Lateran
is the cathedral of the Pope and therefore associated with him as Bishop
of Rome and as Patriarch of the West
St. Peter's Basilica,
the Patriarch of Constantinople
Paul-without-the-Walls Basilica, the Patriarch of Alexandria
St. Mary Major,
the Patriarch of Antioch
(the above 4 Basilicas are the original and primary Basilicas)
Lawrence-outside-the-Walls, the Patriarch of Jerusalem
The church of St.
Francis at Assisi
The church of the
Minor Basilicas are specially linked to the papacy and are to be places of
pastoral zeal and dedication to the liturgy, including the Divine Office
("Liturgy of the Hours"). They have a sanctuary fixture known as a
conopaeum (also called a papilio, pavilion, umbellina, or
sinicchio), a tall, umbrella-like canopy made of alternating bands
of red and yellow silk -- the colors of the papal government -- and topped
with a copper Cross, the original function of which was to shelter the patriarch.
Basilicas are also allowed to have their own coat of arms and can have members
carry a special tower with a small bell in processions. Some famous Minor
Basilicas are Ste. Anne de Beaupré in Québec; Sacré
Coeur in Montmartre, Paris; National Shrine of the Immaculate Conception
in Washington, D.C., etc.
An oratory is a place other than a parish church where it is canonically
permissible to celebrate the Liturgy. Some are totally public, some are
semi-public (such as in monasteries, hospitals, prisons, etc.), and some
are private (in private homes, private oratories can only be set up by permission
of the Pope).
Anyone can set up a chapel -- and there are many varieties of chapels, including
chapels inside larger churches. But to be able to celebrate the Mass in a
private chapel, permission of the Bishop is required. The word "chapel" (and
the word "chaplain") derives from the Latin "cappa," meaning "cloak," in
reference to the chapel built to house a certain
relic -- the half of the cloak that St. Martin
of Tour kept after giving the other half to a beggar.