Hola,
It depends on what you mean by pen. It often happens that the extent of a word meaning in one language is not the same as in another one, so that word forms cannot be translated by word forms, but meanings are translated by meanings, and five different meanings of a word in one language may have five different translations in the other language.
A pen is an ink-based writing instrument. It can be a dip pen, which you dip in ink in order to write, such as a quill, a cane, or a stylus, or it can be a reservoir pen, where the ink is contained in a reservoir inside the pen: such are the fountain pens and the more modern ballpoint pens, roller point pens and all the other variety of newer pens, of which there is a large selection. By contrast, a pencil is a graphite writing instrument, not ink-based, and again, whether it is real graphite or any of the newer synthetic materials is indifferent for this purpose.
Pluma literally means feather, and the name was adopted when the pen used to be a goose feather, that is, a quill. Nowadays, pluma by itself is the metal nib of the pen. By extension, the whole pen is often called a pluma. In many countries it is called a lapicera, instead of pluma.
The proper name for the pen, meaning by pen the instrument that holds the metal nib, is portaplumans, very little used, but nevertheless the correct name.
In Argentina we call lapicera both the fountain pen and the dip pen. We call pluma the nib itself. However, if you call pluma the whole pen, as it is done in other countries, nobody looks at you as if you were a Martian: everybody understands you.
In Spanish, a pencil is called lápiz, and a pen is called lapicera. The different kinds of pen have different names.
Thus, a fountain pen is called a lapicera fuente, lapicera estilográfica o estilógrafo, or simply a fuente. The most common name is a lapicera fuente.
A ballpoint pen is called lapicera a bolilla, bolígrafo or birome. The most common name in Argentina is birome, as Imariano said, in honor of László Biró, its inventor.
In some countries, the pen is called lapicero instead of lapicera, but lapicero is technically a pencil holder, not a pen.
All of these meanings and usages have been checked with different diccionaries and the Dictionary of the Real Academia Española.
I hope it helps, or maybe it confuses you more. Forgive me if it is the latter.
Saludos