Choral mass settings that include all five setions - the Kyrie, Gloria, Credo, Sanctus, Agnus Dei - are normally Roman Catholic. These are sometimes called Missa Solemnis, of which the most well-known example is Beethoven's. Beethoven regarded this work as among his greatest achievements, if not the greatest.
Not all 5-section Masses in the RC tradition are referred to as Missa Solemnis, for example Schubert's Mass 6 in E flat, D 950 does not usually have this description, although I am aware that sometimes it is so described. I would say that this Mass is my favourite of all Masses written by anyone. Even though all of Schubert's masses are in the RC tradition, the Church was wary of using some of them because Schubert insisted on excluding a short section of the Credo, about which I have forgotten the details.
Shorter choral Masses in the RC Church are generally referred to as Missa Brevis. They do not not include all 5 sections, although the Kyrie and Gloria are usually included. They would all normally be in Latin, except I guess some of the more modern ones which may be in the local vernacular.
Lutheran Masses are usually referred to as either Missa Brevis or simply Lutheran Mass, and generally only include the Kyrie and Gloria. Confusingly, several were written in Latin. Therefore, by description only it's not possible to distinguish between an RC Missa Brevis and a Lutheran one. One would need to check the religious leaning of the composer in question, or failing that the exact text that was used, where one would expect to see some differences. For example, it would be much less likely to see any references to the BVM in Lutheran sacred works.
J S Bach was of course a Lutheran and wrote several masses for that Church. However, his Mass in B Minor is a Missa Solemnis in the RC tradition. This magnum opus wasn't written in one go, but was amended at various stages in Bach's career, and I understand that he tended to use as a kind of calling card when trying to impress different prospective employers. It's a magnificent work.