Expansion cards called PCI , both  types below.           

The modern PC has only PCI-e slots now.  (called Express)
The 3 most common usages
are a new very fast GPU Video card, Like my  GTX1050  in the top x16 slot. (or USB3 or SATA-III cards; even bootable !)
next most common is for those with older PCs, 10 years old and you are tried of slow USB port, or sick and tired of you SSD plugged into the pathetic slow SATA1 port. (so we upgrade this)
Some folks what to add in a SATA-III card, because  they ran out of ports or want that modern SSD card to run at full speed.
ISSUES: (lots)
  • On SATA upgrades,  if your mother board is too old the PCI-e slug speed Version 1 only don't bother doing this upgrade,  for SSD drives. It will be bottlenecked badly Unless you buy a X2 card seen just below.
  • On some mobo (Low End, toy grade) do not allow cards in the top x16 slot if not a GPU Video card , your manual on your mobo tell this dirty secret, if true.
  • Some mobo have open ended sockets say X4 and you plug X8 card (too wide) and it works if ? the card detects this and runs only x4 channel lanes, some can some can't ) It's just feature, that can work.
  • Some mobo, have a x8 slot that is only wired to x4 channels, My z600 has that.
Watch out for a mobo the make the  boot ROM on your SATA-III card useless and will not boot to it , or you have 2 or 3 addin cards all wanting ROM space, (video, SAS RAID and then you add SATA-III with its ROM(boot)
The space for rom can be  limted to 128- 196k bytes, that can vary, as the mobo and all BIOS and boot rom and Int.13 video ROM must all fit inside the 1MByte space allocated to 1MB, limitation on OPROM size, total. There is no sure thing here, try it yourself.
Some mobo BIOS have bit selection for "Enable Option ROM"  make sure that is on. See the 11 pins below, that is very nice X2 card that will scream any SSD made, (modern)  The chip is Marvell™
Like Raid cards (SAS) the best boot ROMs have  hot key, like Control +M or (+L) or some key  that allows you speed up the scan or limit the scans for boot drives. (and even shows what drives it found  live booting messages, wow)
The 9215 chip is x1 only. and $10 less, Hardly worth getting that. IMO

This same cards above are also sold in full blown RAID, version, and may work better due to a more advanced BIOS ROM. In all cases own A PC that is 10 year old or less. (support reasons)
In all cases having a smarter ROM BIOS can be a god send. (for sure if you hate long boot delays) learn that 4 drives that take 10 seconds to spin up, and are sequenced 1 at a time to prevent PSU overload, will take 40second just to get to step 2.
The ROM does not have list of 25,000 HDD drives made in 2 decades, with startup delays, sorry it does not, so has fixed delay for he slowest one made. (change it if you don't  like it)
Speed spec.table (wiki)  One great card I have for SATA-III speeds,  uses a  Marvell chip #88SE9235 R1.1 ( runs 2 channels X2 express and version 2,PCI speeds. 1GB/s. (the other chip by them 9215 is x1 express only)
No matter what card you use, it can not go faster than the Mother board allows.(version-wise v1/v2  and x1/x2 sharing)
It is year 2018, now not 2007, so chips are 10x better now. (do not read old www , posts  10 years old ok?) Worst of all is reading reviews with no date stamp on the review, wow, what useless information that is....lacking  date. (IMO) "Technology is not static"
I highly recommend the    Marvell chip #88SE9235 based cards, sold by many  names (card makers names) but the ship is great if inserted in to  express slots V2 up. If V1 mobo don't bother bother buying this card.
A great reason to use the SATA card is to gain bus speed. (PCI-e side) (if you PC is only express v1, you need x2 card ) See that chart above, stay out of the 250 Box for SSD drives.
Watch out for sellers, showing X2 card /chip and  is lie and is X1, look for and count the  11 pins (x2) on the right edge connector, for the real truth. See what chip is there and read its datasheet, slowly.
This one card is good:  SYBA SI-PEX40063
More information soon on Marvell performance and more photos showing it working  live. 
The Marvell RAID hot key is "Control +M" at boot time. (we will see) I am testing many solutions to gaining best speeds on any SSD drive (HDD is hopeless, here, HDD are slow and will always be so)
Windows 10 install media finds this controller if you pretend to do and install and STOP HERE,  and my SSD no problems, so fresh loads easy. (photo 1)
If I take my SDD with W10  on it already , it fails, too boot (yes does boot but Windows, BSODs)  next is start up  repair that fails, so last I do the 3 times power on trick pick this then  this. and #4 SAFE mode.  and hit the startup-setting, 
I go in to safe mode and it works ok and last restart PC and all is good.
Ok the system is back to normal OLD HDD , moved to below card,  see Ven/DEV code.  ASmedia chip X1 lane, ASM1062  (at MS.com PnP server here)
I have tested this disk on my systems , and chip (SATA) RAID cards and now this card and all do this speed.  (my stock v1 Sata port does 1/2 this)
There are other solutions to SSD speed on SATA-III SDD, and that is using a very fast SAS RAID card, that has X8 lanes. (SAS runs SATA no problems even the LSI9211, does that and is same price as above card) See me do that here.
SATA is a subset of SAS, so use that hardware, and can be cheaper to buy, for sure used, from old server farms that upgraded and this hardware is laying around gathering dust,  buy it run it be amazed.

This is all basic information on PCs , no magic, and is standard of the industry.

All modern systems use this type of Express card.  X16 Is commonly used  for nice upgraded video cards (GPU) (x1 means "by 1 lane", or 1 channel, and can read and write at the same time, unlike old PCI)

OLD PCI below:  Nobody uses this anymore, but I put it here to show that you must never use the cards above, down here.
32bit speeds are limited to 133 MB/s, and 2 times that for the 66MHz versions)  (You can read or write but not at the same time so through-put is limited)

The 2 notch version below left is best to have (seen in the wild common)32bit, (64bit is and was rare, because Express came out at that time, making the below useless  )
Legacy Old PCI (non express)

version 1.  9-9-2018