In Figure 1. we have an example of the first case for the symbol 1: ie a grid with 4 rows (2,4,7,8) where the symbol 1 occurs only in the same 4 columns (1,3,5,6).

Look at each row in turn. 
Row 2: all the 2s are in columns 1,3,5,6. 
Row 3: all the 2s are in columns 1,3,5,6. 
Row 5: all the 2s are in columns 1,3,5,6. 
Row 6: all the 2s are in columns 1,3,5,6. 

Columns 1,3,5,6. must provide the 1s for rows 2,4,7,8 
so any other 1s in these columns can be removed. 
There is one in column 1 and three in column 5.

Understanding Jellyfish

To understand Jellyfish please read the explanation for Swordfish and then extend it to 4 columns and 4 rows. The arguments are identical but the variations are more extensive and it would serve little purpose to go through them all in detail. For Jellyfish we must have a situation in which for 4 columns the symbol S is restricted to the same 4 rows. To satisfy the requirement of 1 S in each of these columns we are forced to use one of the 4! possible arrangements and any other Ss on these rows can be removed.

SSSS
SSSS
SSSS
SSSS

Possible solution:

S---
-S--
--S-
---S

etc (24 of them in total).

Possible column arrangement:

SS
 SSS
 SS
SS S