A SIV is a type of SPV, most commonly associated with having CDO and other longer-termed assets. The main benefit of them is that you make a rate play, using higher-rate assets funded by short-term, lower rate, liabilities. SIVs aren’t to be confused with traditional conduits, which have liquidity agreements and lines of credit (commonly known as LIQ/LOC agreements), which means the host banks support them either through funding of good assets (LIQ) or bad ones (LOC). SIVs usually do not have that support, but with recent events SIVs have been supported by the banks.
Both SIVs and traditional conduits are SPVs, but the CP market that funds them accounts for the lack of SIV bank supports by charging the issuer more spread for the CP issued, especially now.
SPVs are the broad category of vehicles that can qualify as on balance-sheet, or off. Off balance sheet SPVs are usually Qualified SPV(E) vehicles, governed by FAS140. Not all SPVs are QSPV(E)s, they have to qualify under certain circumstances to be eligible for FAS140.
SPVs are used for a broad range of items, from term securitization issuance, conduit securitization issuance, and other entities. They are most infamously known for Enron using them to hide derivatives, liabilities, and manipulating earnings.
FAS140 has been in a “rework” mode for the past 3 or so years. FASB is planning on changing the structure of the QSPE to bring it more in alignment with international accounting standards and also eliminate some of the trickery.