What's the difference between distributed hashtable technology and the bitcoin blockchain?
Distributed Hash Table
A DHT is simply a key-value store distributed accross a number of nodes in a network. The keys are distributed among nodes with a deterministic algorithm. Each node is responsible for a portion of the hash table.
A routing algorithm allows to perform requests in the hash table without knowing every node of the network.
For exemple in the Chord DHT —which is relatively simple DHT implementation— each node is assigned an identifier and is responsible of keys which are closer to its identifier.
Imagine there is 4 nodes that have identifiers: 2a6c, 7811, a20f, e9c3 The data with the identifier 2c92 will be stored on the node 2a6c.
Imagine now that you only know the node 7811 and you are looking for the data with the identifier eabc.
You ask the node 7811 for the data eabc. 7811 doesn't have it so it ask the node e9c3 wich send it to node 7811 which send it back to you.
A clever algorithm allows to find data in O(log(N)) jumps. Without storing the entire routing table of the network (the addresses of each nodes). Basically you ask the closest node to the data identifier you know wich itself asks the closest node it knows and so on reducing the size of the jump at each step.
A DHT is very scalable because the data are uniformly distributed among nodes and lookup time generally grows in O(log(N)).
Blockchain
A blockchain is also a distributed data structure but its purpose is completely different.
Think of it as a history, or a ledger. The purpose is to store a continuously-growing list of record without the possibility of tampering and revision.
It is mainly used in the bitcoin currency system for keeping track of transactions. Its property of being tamper-proof let everybody know the exact balance of an account by knowing its history of transaction.
In a blockchain, each node of the network stores the full data. So it is absolutely not the same idea as the DHT in which data are divided among nodes. Every new entry in the blockchain must be validated by a process called mining whose details are out of the scope of this answer but this process insure consensus of the data.
The two structures are both distributed data structure but serve different purposes. DHT aims to provide an efficient (in term of lookup time and storage footprint) structure to divide data on a network and blockchain aims to provide a tamper-proof data structure.