I'm assuming you mean DNA sequencing (excluding things like RNA-seq).
Is Sanger sequencing the first generation?
From Metzker 2010:
The automated Sanger method is considered as a "first-generation" technology
Some of the technology that was in development when this review was written is no longer in development, but this is still an excellent review and a great place to start.
Is second generation sequencing the same as next generation sequencing?
Also from Metzker 2010:
and newer methods are referred to as next-generation sequencing (NGS).
The "newer methods" in the review are:
- Emulsion PCR based like Roche/454
- Solid phase amplification like Illumina/Solexa
- Single molecule like Helicos BioSciences and Pacific Biosciences
As of today, is there any commercial 3rd generation sequencing technology in use (or is it still in development)?
The development of single molecule methods (third item in the above list) has historically taken longer than the other two, so sometimes they are referred to as third generation. However, note how Metzker above considers them all "next-gen".
A recent paper from PacBio itself makes the distinction of halting:
Second-generation sequencing (SGS): Sequencing of an ensemble of DNA molecules with wash-and-scan techniques.
Third-generation sequencing (TGS): Sequencing single DNA molecules without the need to halt between read steps (whether enzymatic or otherwise).
Ultimately, I think the "generations" are more useful to make the "Sanger vs. Not Sanger" distinction. Sanger sequencing is very different than next-gen in terms of what kind of experiment you can do and what sort of data you obtain.
Past that, the number of a generation is more of a marketing term. For instance, at the bottom of the PacBio paper:
Conflict of Interest statement. All authors are employees of Pacific Biosciences and own stock in the company.
In practice, PacBio competes with second generation platforms. It is in their interest to say their technology is on "another level" compared to what's available on the market, but in practice, this is debatable.
Anyhow, to answer your question:
- There is a technology in use and commercially available which has been referred to as third gen (PacBio)
- There was a technology in development that falls under most definitions of third gen (Helicos), which went bankrupt in 2012
- There is a technology in development (ON MinION) that is single-molecule based and was introduced after PacBio, so if PacBio is third generations, so is MinION (although the MinION is apparently very different from PacBio)