RAM for servers comes with a few common metrics to specify it's capacity and ability to work in a particular configuration. To help confuse this there are different names for what is essentially the same thing, and the "standard" name changes depending on which type of RAM you're using.
Capacity (1GB, 4GB, 32GB, etc)
This is easy enough; everyone should already be familiar with the concept that RAM comes in different capacities. The particular type of RAM determines what the maximum size of a single stick can be, but that's irrelevant because actual implementations limit the amount of RAM a system can support (ie, check the documentation for your system to see what capacity it supports).
RAM's capacity can be organized in different configurations. Usually there's just one standard configuration for RAM of a certain size. If you're buying ultra-cheap RAM off the Internet be warned that it may be non-standard (especially if they mention the organization) and not supported by your server.
Speed (1600MHz, etc)
For the purposes of this Answer, you want the speed of the RAM to match the maximum speed of the system. RAM that is one or sometimes two "speeds" faster will work as well, though at the lesser speed. Similarly RAM that is one or two "speeds" slower will work, also at the lesser speed.
Integrity Protection (ECC or Non-ECC)
ECC is the most common form of integrity protection (ie, making sure cosmic rays didn't flip any bits and none of the memory locations are going bad). In most systems the RAM must either be ECC or non-ECC, whatever the system requires. Occasionally this is called 72-bit memory (a misnomer leftover from 64 memory data channels getting 8 bits of ECC along side the data bus).
When RAM has ECC, that protection information can be checked at a variety of times. The most basic protection reads and checks the ECC data only when the RAM at that memory location is read. More advanced options allow the system to check ECC regularly. Most frequently I've seen this called "memory scrubbing"; it works much like disk array scrubbing; and like disk array scrubbing you should have it enabled unless there's a good reason to disable it.
ECC is one of the steps reducing the impact of Row Hammer bug.
Bus Electrical Capacity (Unbuffered or Registered)
We're not electrical engineers, so all you really need to know is that Buffered or Registered RAM allows more RAM in a system than without. Like ECC this is something that must be supported by the system. Unlike ECC many new servers support both Unbuffered/Unregistered and Buffered/Registered RAM. Older servers tended to support only one or the other. Registers are a type of buffer, but the terms are used interchangeably when applied to RAM. I have never see a system that can mix Unbuffered and Registered at the same time.
When you see UDIMM, the "U" is for "Unbuffered". The "R" in RDIMM is "Registered".
Ranks
Registered RAM has well defined electrical "usage" characteristics metered in "ranks". Each RAM channel (or bus) in a system can support so many ranks at each speed it supports. Typically systems are rated at two speeds (ie, the channel runs at X speed normally with up to A ranks; but Y speed if over that; and only up to B ranks are possible).
There is RAM available with the same capacity and speed, but taking up different numbers of ranks. Typically the more capacity the more ranks a module takes up. Low voltage modules take up less ranks (per the module's specifications).
Foot Notes
There are a variety of configuration options unrelated to what physical RAM you need to buy for your server. These include mirroring the RAM (just like RAID1, but for RAM), sparing (literally spare RAM that if one goes bad the spare replaces it), timing and related optimizations.
Modern servers typically have the memory controller(s) integrated into the CPU instead of a separate North Bridge chip. This means systems that support multiple CPUs must have the CPU socket populated that corresponds to a memory slot in order to use that slot. Similarly some CPUs required there to be memory populated in their slots for the system to work. See the system's documentation for details.
Modern servers typically have more than one memory channel. These channels operate mostly independently, which will allow greater memory bandwidth in memory-intensive usage scenarios. Generally you should plan on distributing memory across all channels on all populated CPUs as evenly as is realistic to ensure the best performance.
I ended up finding the answer to this one is a no, you don't need to use HP/HPE SmartMemory in the Proliant DL320e Gen8 v2 after getting someone in the server room to hook me up with the part number on the pre-installed RAM sticks. HP didn't even provide us their own HP SmartMemory... They gave us a 4GB stick of this, which isn't even supposed to be something they sell, with 8GB being the supposed minimum config:
Micron 4GB PC3-12800 DDR3-1600MHz ECC Unbuffered CL11 240-Pin DIMM
Dual Rank Memory Module Mfr P/N MT18JSF51272AZ-1G6K1ZE
Unless they just forgot to slap their HP/HPE SmartMemory sticker over Micron's label ;) haha. You tell me shrug Oh and that missing 4 gigs of RAM too... I still don't feel too confident with this answer, but it's better than nothing. I'm kind of suspicious that someone took some liberties with idle hardware, but only because I can't prove that the stick the guy sent me was what HP actually shipped them off with.
Best Answer
Yes, it will. ASSUMING IT FITS - and given that pretty much any rack server is using a different standard than desktop machines, the answer is.... most likely not.
And the detailed answer is: Read the manuals.
As in: You state "I have found this PDF which explains memory requirements. It however does not mention ECC, NonECC etc."
Did you search? Because ONE google search ("Dell R710 manual" - hardly arcane) pointed me to https://downloads.dell.com/manuals/all-products/esuprt_ser_stor_net/esuprt_poweredge/poweredge-r710_owner%27s%20manual_en-us.pdf, which is the complete owners manual.
Page 129 talks quite clear what is needed:
Not using the manual makes me want to close this - seriously, whether you have worked with rack servers or not, you should ALWAYS try to read the manual. Btw., the page goes on with specifying what sizes and hoe many modules fit etc. - read it.
Anyhow, you can fit any RAM that matches the description. Have fun finding a desktop system using RDIMM. And as i says, you need alternatively ECC UDIMM.