What is the difference between substitution cipher and block cipher? I'm studying(and clearing my head) about block cipher. I started from Caesar Cipher which can be considered as a kind of substitution cipher (if my understanding is right).

And an ideal substitution cipher (in 26 alphabets) is the two functions $E(x,k)$ and $D(x,k)$ where $0 \leq k &lt; 26!$. And given $k$, one of the bijection(substitution) functions is (uniformly)selected and used to substitute a letter.

What I thought here is that this is also a block cipher. (1 letter is 1 block)
I read https://en.wikipedia.org/wiki/Substitution_cipher and it says


  Although the number of possible keys is very large ($26! \approx 2^{88.4}$, or
  about 88 bits), this cipher is not very strong, and is easily broken.
  Provided the message is of reasonable length (see below), the
  cryptanalyst can deduce the probable meaning of the most common
  symbols by analyzing the frequency distribution of the
  ciphertext—frequency analysis.


I feel this description is talking about the problem of ECB mode in block cipher.

So my understanding so far is that substitution cipher can be considered as a block cipher. But I'm wondering if a block cipher is always substitution cipher.

What is the difference between them in general.
I feel this description is talking about the problem of ECB mode in block cipher.
So my understanding so far is that substitution cipher can be considered as a block cipher. But I'm wondering if a block cipher is always substitution cipher.

(1) let us compare a block cipher with ECB mode to a substitution cipher.
With ECB Mode and a given key, a block cipher can be seen as a substitution cipher which maps one block to another block. For example, AES, twofish, or serpent has a block size of 128 bits; you may say, &quot;one 128-bit block is substituted to another 128-bit block&quot;. 
(Note: this is just a simple comparison. If a block cipher has a &quot;state&quot;, the same input blocks might get different output blocks. In this case, the block cipher might be compared to Vigenère cipher.)
While a Caesar Cipher maps one letter to another letter. That is from a 5-bit to a 5-bit, or at most a byte to a byte. (From this point, you could be right to say &quot;substitution cipher can be considered as a block cipher&quot;; but the block size is quite small.)
So, I might say a Caesar Cipher is a special block cipher which has a small block size; or, on the other hand, a 128-bit block cipher (with ECB mode) is a &quot;monster Caesar Cipher with 2128 letters&quot;.
(2) a block cipher with certain mode (except ECB) 
This is a fun part. From my point of view, if you want, you can actually create a Caesar Cipher with CBC, PCBC, OFB, CFB, CTR modes by replacing the IV or counter with a letter.

What is the difference between them in general.

(3) difference 
They are quite different in practice.
But the main one is size: block size, key size, IV size, and counter size. (The last two is really the block size for different uses). 
If a monster Caesar Cipher has 2128 letters and has CBC, PCBC, OFB, CFB, CTR modes, it might be as strong as a 128-bit block cipher.