I understand the root DNS servers (A to M). What I don't exactly get it is the difference between, let's say the "F Root DNS" and the "A Root DNS".
Why is there 49 total "F" DNS's and only "A" DNS's?
Isn't the DNS record database from A to M the same?
Because of vital importance, high load and especially because of need to tolerate any possibly DDoS attack, internet have many root servers.
All root servers store the same DNS database.
A through M is total of 13 nameservers, but to be exact each this "nameserver" is not actually a server, but it is an IP address.
For most of root servers, that IP address corresponds not to single machine, but it is a so-called anycast address - address which can be routed to any of several locations around the globe. Thus when you query, say f.root-servers.net, your query may be answered by a server located at any of this anycast sites (usually the one nearest to your).
"A" root server is also anycasted.
Different root servers (A, F etc.) operated by different organisations, thus lowering possibility of some human mistake to take down the whole internet.
There's a map of root server locations on root-servers.org.
Georedundancy, in short.
Root queries use anycasting to select a closeby root instance.