Gene and Protein isoform
The term isoform has become a little ambiguous over the years (see http://blogs.cornell.edu/collinslab/2012/05/30/protein-isoform/)... still some things are consistent:


In some genetics literature 'isoform' has been used in the place of allele when talking about the allele states at a locus for a gene
Typically a gene isoform is equivalent an alternate transcript. The gene isoforms are the set of mRNAs that can be produced by a gene.
Protein isoform commonly refers to the set of proteins produced by a gene, this can include variations produced by alternative splicing and post-translational modification. Note that in some contexts the set of products from closely related gene duplications can also be included.


Note that databases will typically have a specific definition in mind for their use of isoform in their annotation, check their documentation for details (e.g. in UniProt see What is the canonical sequence? Are all isoforms described in one entry?)