Good thinking! To answer your questions, all proteins come from genes, however, a single gene can encode for several forms of a single protein. These are called splice variants and are a result of alternate splicing by the splicisome during transcription resulting in slightly different proteins that may have vastly different functions. These proteins are often referred to as iso forms.

Additionally, a single gene can produce a single protein during translation but that protein can then be altered in a manner that is referred to as post-translational modification. There are many different modifications that can occur (phosphoryltation, gylcosylation, etc.) however if the protein is post translationally cleaved it could become a similar protein as the original product but have a very different structure or function. Hope this answers your questions.

As you ask, there are some genes that code for more than one protein. This can happen in two ways:
- initiation sequences at different points in a DNA strand that are frame shifted from other initiation sequences, causing the transcription proteins to get up to three different proteins from a single section of DNA, and
- also the alteration of protein strands subsequent to translation, including different attachments to other proteins, sugars, lipids, and even simply in different geometries of itself.