Vendors call it a lot of things but you want to look for G.652 compliant fiber for most SMF applications.
If you need a G.653-657 you are doing something pretty specialized.
Single mode has a MUCH smaller core ( 9 micron IIRC) than MMF.
While that covers the transmission characteristics you have myriad options for different environments ( you want it in the air on poles or direct bury ? do you have a need for more bend insensitivty ? is it in a space that carries air and as such needs to be plenum rated (doesn't outgas nasty things and choke you in event of fire)
You really need a good cabling vendor with BICSI certification to help in properly selecting any part of your cable plant IMHO
In my enterprise i've stopped using OM3 in favor of OM4 for all my multi mode applications as I tend to be married to a fiber plant for years and I like to build in as much head room as I can afford.
The 60,000 ft overview of MMF vs SMF is as such:
Single mode has much smaller core and is design to carry 1 ray of light (mode) in as straight a line as possible.
Multimode has a , comparatively, larger core than SMF and the rays bounce from outside edge to outside edge of the fiber while in transit.
Single mode is generally used where longer than campus distances are required.
Multi mode systems generally cost less and work great at shorter distances.
Distances quoted for any type of fiber don't take into account the impact to your optical power budget of any splices or connectors in the path. That is to say if you have fiber from a to b and fiber from b to c and you jumper between fibers to connect A to C you loose power compared to a fiber run directly from A to C.
You MUST buy the correct optics for the fiber you are using*
* yes there are conditioning cables but they are a kludge with lost of limitations and you won't find them in my cable plant.
