Spatial multiplexing is the process where the same informaiton is placed across 2 or more of the available antennas in an AP or Client device.
Using this simple definition almost all of the operating modes on a device use spatial multiplexing.
Good diagrams found here:
http://www.arubanetworks.com/pdf/technology/whitepapers/WP_80211acInDepth.pdf
When you have a multistream capable AP talking to a single stream device it can use CDD (Cyclic Delay Diversity aka Cyclic shift diversity) or STBC (Space time block coding)
For CDD sending to a single client the AP transmits a time delayed copy of the single stream on all antennas with time delays on the order of the OFDM symbol period (3.2 microseconds). the time delays are defined in the standard. The time delays decorrelate the copies of the signal being sent so this means that there is no (or very little) beamforming occuring. Beamforming in this case would be detrmental since the AP has no information on where the user is.
For STBC one stream is sent over 2 antennas or two streams over 4 antennas. there is no time delay across the signals but the data on the two antennas is decorrelated mathematically using something called an Alamouti code
https://en.wikipedia.org/wiki/Space%E2%80%93time_block_code#Alamouti.27s_code
again due to the decorrelation of the signals there is no beamforming and the element pattern of the AP dictates the antenna characteristic.
For Tx BF and MU MIMO
In 11ac there is a sounding process the sounding process gives the AP a mathematical recipe for ampitude and phase on each antenna for each stream so that the signal peaks directly over the target antenna(s) on the client. In this situation the signal are correlated and the signals from the antennas are combined to form beams and to maximise the ability of the system to support more than one stream.
Tx BF and MU MIMO are very closely related technologies. The underlying math for both is the same.
The sounding process allws the AP to create orthognal antenna patterns for each stream that is being sent. In appropriate enviornments (like an indoor space with walls ceiling and floor) the system works to deliver near ideal Multi-Stream/Multi User support.
So to summarize
in the simplest sense spatial multiplexing is transmitting signal on multiple antennas that are tied to the same baseband.
CDD/CSD and STBC do this without beamforming
Signal are de correlated either with large time delays or by mathematical encoding
TxBF and MU MIMO do this with beamforming
Signals are correlated and orthogonal beams are formed
Further reading
3 articles starting with this one
http://community.arubanetworks.com/t5/Technology-Blog/Wave-2-Antennas-in-the-spotlight/ba-p/228089
and an Airheads deep dive on 11ac
https://www.youtube.com/watch?v=HFo67dEGfcY