There exists a spectrum of expertise between programming and biology on which all bioinformaticians lie. Some are programmers who know a smidge of biology, others are biologists who can hack together a few lines of R to do analysis, and there's a broad range in between.
If used correctly, scientific programmer strikes me as a position where you're going to be writing code, but not so much involved in the scientific direction of the lab. They've got ideas, they want you to turn them into working scripts. Reading the description and talking to the folks involved is going to be crucial to defining your potential role.
Both terms are also very vague, so trying to define the exact job description based on these job titles is futile.
A bioinformatician, or a scientific programmer in biology, could be be working on a very wide range of topics, from marine ecology to cancer genomics.
His job could run the gamut from analyst to software developer to database administrator.
Given the explosion of genomic data, many associate bioinformatics with the analysis of next-generation sequencing data, but this is just one subfield of bioinformatics.
You should really read the specifics of a job offer to understand what the job entails, rather than rely on the job title.
I would venture to say that both job titles are so ill-defined, that they are virtually meaningless.
EDIT. I'll edit my post to say that the job title "Scientific programmer" does include the work programming, so an accent is put on programming. There are a surprising number of self-described bioinformaticians who do little programming other than simple scripts, so that might be one distinction between the two job titles. Still, the titles are so vague that is best to read the job description accompanying the job offer, rather than rely on the job title.