how I can split a column of a pyspark dataframe with whitspace?

You can get the desired result using higher-order function transform

from pyspark.sql import functions as F
df = spark.createDataFrame(
    [('ab', 'summer hot, best friend, not possible, apple, let it go', "let be hot"),
     ('cd', 'do it better, I am sa', "I need to go"),
     ('fg', 'my best post, fun sunday', "it's great")],
    ['key', 'col1', 'col2'])

c1_arr = F.split('col1', ', *')
c2_arr = F.split('col2', ' ')
arr_of_struct = F.transform(
    c1_arr,
    lambda x: F.struct(
        F.size(F.array_intersect(c2_arr, F.split(x, ' '))).alias('cnt'),
        x.alias('val'),
    )
)
top_val = F.sort_array(arr_of_struct, False)[0]
df = df.withColumn('match', F.when(top_val['cnt'] > 0, top_val['val']))

df.show(truncate=0)
# +---+-------------------------------------------------------+------------+----------+
# |key|col1                                                   |col2        |match     |
# +---+-------------------------------------------------------+------------+----------+
# |ab |summer hot, best friend, not possible, apple, let it go|let be hot  |summer hot|
# |cd |do it better, I am sa                                  |I need to go|I am sa   |
# |fg |my best post, fun sunday                               |it's great  |null      |
# +---+-------------------------------------------------------+------------+----------+

It covers what was asked in the question, and it should be fine as per your comments, that you don't care which of max-match values from col1 will go into the result. But for what it's worth, I should show that the script is not identic, there are some strange edge cases which would work differently:

from pyspark.sql import functions as F
df = spark.createDataFrame(
    [('ab', 'summer hot, best friend, not possible, apple, let it go', "let be hot"),
     ('cd', 'do it better, I am sa', "I need to go"),
     ('ed', 'q w,e r,t y', "q e r"),
     ('zz', 'q w,e r, p p o, t y', "q e r p o"),
     ('yy', 'q w,p p o, e r, t y', "q e r p o"),
     ('cc', 'q w,e r p,   e r y', "e e r"),
     ('vv', 'q w,e r y,   e r p', "e e r"),
     ('fg', 'my best post, fun sunday', "it's great")],
    ['key', 'col1', 'col2'])


df = df.toPandas()

import pandas as pd
import numpy as np
df["col2_set"] = df["col2"].apply(lambda x: set(x.split(" ")))
def setter(x):
    data = x.col1.split(",")
    res = np.array([len(x.col2_set.intersection(y.split(" "))) for y in data])
    if res.sum() == 0:
        return None
    else:
        return data[res.argmax()]
df['match_pandas'] = df.apply(lambda x: setter(x), axis=1)
df.drop(columns=['col2_set'], inplace=True)

df = spark.createDataFrame(df)

c1_arr = F.split('col1', ', *')
c2_arr = F.split('col2', ' ')
arr_of_struct = F.transform(
    c1_arr,
    lambda x: F.struct(
        F.size(F.array_intersect(c2_arr, F.split(x, ' '))).alias('cnt'),
        x.alias('val'),
    )
)
top_val = F.sort_array(arr_of_struct, False)[0]
df = df.withColumn('match_spark', F.when(top_val['cnt'] > 0, top_val['val']))

df.show(truncate=0)
# +---+-------------------------------------------------------+------------+------------+-----------+
# |key|col1                                                   |col2        |match_pandas|match_spark|
# +---+-------------------------------------------------------+------------+------------+-----------+
# |ab |summer hot, best friend, not possible, apple, let it go|let be hot  |summer hot  |summer hot |
# |cd |do it better, I am sa                                  |I need to go| I am sa    |I am sa    |
# |ed |q w,e r,t y                                            |q e r       |e r         |e r        |
# |zz |q w,e r, p p o, t y                                    |q e r p o   |e r         |p p o      |
# |yy |q w,p p o, e r, t y                                    |q e r p o   |p p o       |p p o      |
# |cc |q w,e r p,   e r y                                     |e e r       |e r p       |e r y      |
# |vv |q w,e r y,   e r p                                     |e e r       |e r y       |e r y      |
# |fg |my best post, fun sunday                               |it's great  |null        |null       |
# +---+-------------------------------------------------------+------------+------------+-----------+