A really really simple guide to types of storage.
Local Disk (HDD):
A disc or number of discs called platters store data, in the from of "0"s and "1"s, and an arm with a head is used to read and write data to the platters. HDDs are a type of Directly Attached Storage (DAS).
Local Disk (SDD):
Solid State Drives (SSD) don't have any mechanical parts. A super simple way of thinking about the way SSDs work is think about lot's of cells which have the ability to store "0" or "1". Each cell has an address. The address is called and the value from that cell returned. SSDs perform faster than HDDs. SSDs are more reliable, they consume less power but cost more that HDDs. SSDs are a type of Directly Attached Storage (DAS).
Network Attached Storage is basically one or many HDDs or SSDs inside a box with some special software. NAS is connected over Ethernet. NAS appears to a computer that connect to it as a "file share" i.e. the computer knows this file store is not attached directly to the computer but somewhere on the network.
Storage Attached Network is basically one or many HDDs or SSDs inside a special box called a SAN array. SAN storage technology has it's own network technologies similar to Ethernet but using completely different protocols. So for example you can by a SAN switch etc. A computer can access SAN storage via connecting it to the SAN network via special hardware in the computer called a Host Bus Adaptor. SAN usually appears to the computer as if it was directly attached to the computer. Given the need for special hardware the cost of SAN can be very expensive but performance is much better than NAS. SAN vs DAS is a more complex subject that isn't worth going into right now.
There are other storage technologies out there but the ones listed above are the most prevalent. No other technology has had a major breakthrough.