The difference
Dogma always has a direct impact on the possibility of our salvation. Dogma has Christ God as it's source. (The teachings of..., the works of..., the precedence of...) As taught directly by the Apostles... and which none of them, nor the Churches that they taught directly, disagreed.
Simple Examples:
The Trinity
The Death, burial and resurrection on the third day.
Baptism
These are known as Holy (T)radition. As a byproduct of what they are, Christians are not allowed to deny them. These are the things "set" by Christ as the proper path for his followers. We are not to be at odds with the Masters teachings.
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Doctrines are always the teachings of men, who have studied the scriptures in hopes of finding answers to their questions, with the intention of having them accepted as truth. Doctrines are always subsets to DOGMA, and they are not directly related to salvation.
Simple Examples:
The ascension of Mary (that's an Orthodox one for good measure)
Timing of the tribulation (everybody has an opinion on this one)
Method of baptism (everybody has an opinion on this one)
Sola Scriptura
Someone mentioned "Celibate Clergy"... This is neither, as it is not a "teaching" but rather a monastic "discipline". All of these and "what color should the flowers be" are lower (t)raditions. Take them or leave them.
Many Doctrines that have no root in "The Church" teaching from the beginning, and were masquerading as DOGMA, have been put to the test by councils. These incorrect teachings, when they are found, are labeled "heresy", which means to "pick and choose". For the fathers of the Church, this pointed to the idea that a person had "cherry picked" a subject from scripture, thought that they understood it correctly, and was actively teaching it to others from the ALTAR. Most teachers of heresy recant and the matter is put to rest. After all, most are just simple errors.
Occasionally, we have in history clergy or teachers who stand out and will not change their position on such a subject. These are called before the same councils (most of them will not show up) and the council deliberates. After several attempts are made (usually three) the person himself is labeled a "heretic" (a teacher of heresy) and accepts his fate as excommunicate. That is to say that he can no longer gather with the Christians and take part in communion. This is done to protect others.
The local Churches will affirm that he is anathema. The word "anathema" means "to be left outside". It carries the context of the wedding guest who was without answer when the King ask him why he had no wedding garment. (Matthew 22)
It has come to be something much stronger through the years. Some misinterpret the word as "to be damned". That is what many say is the only possability for those who have been excommunicated, but that is only Doctrine not DOGMA.
Forgive me...