A very high level difference is that merge() is used to combine two (or more) dataframes on the basis of values of common columns (indices can also be used, use left_index=True and/or right_index=True), and concat() is used to append one (or more) dataframes one below the other (or sideways, depending on whether the axis option is set to 0 or 1).
join() is used to merge 2 dataframes on the basis of the index; instead of using merge() with the option left_index=True we can use join().
For example:
df1 = pd.DataFrame({'Key': ['b', 'b', 'a', 'c', 'a', 'a', 'b'], 'data1': range(7)})
df1:
Key data1
0 b 0
1 b 1
2 a 2
3 c 3
4 a 4
5 a 5
6 b 6
df2 = pd.DataFrame({'Key': ['a', 'b', 'd'], 'data2': range(3)})
df2:
Key data2
0 a 0
1 b 1
2 d 2
#Merge
# The 2 dataframes are merged on the basis of values in column "Key" as it is
# a common column in 2 dataframes
pd.merge(df1, df2)
Key data1 data2
0 b 0 1
1 b 1 1
2 b 6 1
3 a 2 0
4 a 4 0
5 a 5 0
#Concat
# df2 dataframe is appended at the bottom of df1
pd.concat([df1, df2])
Key data1 data2
0 b 0 NaN
1 b 1 NaN
2 a 2 NaN
3 c 3 NaN
4 a 4 NaN
5 a 5 NaN
6 b 6 NaN
0 a Nan 0
1 b Nan 1
2 d Nan 2