for method 1, the order of execution is

update user where id = 1   ------------------------- (1)
insert log (id,xxx) select x where user id = 1 ------(2)

suppose there are two things An and B, and their order of execution for operations 1 and 2 is as follows:

------------A------------------------------------------B------------------
----user.id=1X-----------------------------------------------------
------------------------------user.id=1XB----
---X------------------------------------------------
-------------------------------user.id=1X-------------

because everything blocks waiting at operation (1), 10 things are executed in series, and there is no deadlock.

for method 2, the deadlock analysis is as follows:
first analyze the deadlock log

-sharp
show engine innodb status;


=====================================
2018-10-31 10:36:02 7faef1990700 INNODB MONITOR OUTPUT
=====================================
Per second averages calculated from the last 5 seconds
-----------------
BACKGROUND THREAD
-----------------
srv_master_thread loops: 59 srv_active, 0 srv_shutdown, 3933403 srv_idle
srv_master_thread log flush and writes: 3933462
----------
SEMAPHORES
----------
OS WAIT ARRAY INFO: reservation count 123
OS WAIT ARRAY INFO: signal count 106
Mutex spin waits 110, rounds 1151, OS waits 25
RW-shared spins 94, rounds 2817, OS waits 93
RW-excl spins 6, rounds 166, OS waits 5
Spin rounds per wait: 10.46 mutex, 29.97 RW-shared, 27.67 RW-excl
------------------------
LATEST DETECTED DEADLOCK
------------------------
2018-10-31 10:26:48 7faef190e700
*** (1) TRANSACTION:
TRANSACTION 24058981, ACTIVE 8 sec starting index read
mysql tables in use 1, locked 1
LOCK WAIT 5 lock struct(s), heap size 1184, 2 row lock(s), undo log entries 1
MySQL thread id 358, OS thread handle 0x7faef0298700, query id 76122 192.168.2.127 root updating
update t_user
    set score = score + 6
    where id = 1
*** (1) WAITING FOR THIS LOCK TO BE GRANTED:
RECORD LOCKS space id 9890 page no 3 n bits 72 index `PRIMARY` of table `ahamp-cms`.`t_user` trx id 24058981 lock_mode X locks rec but not gap waiting
Record lock, heap no 2 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
 0: len 4; hex 80000001; asc     ;;
 1: len 6; hex 0000016f1c5d; asc    o ];;
 2: len 7; hex 75000001481517; asc u   H  ;;
 3: len 4; hex 74657374; asc test;;
 4: len 4; hex 80000037; asc    7;;

*** (2) TRANSACTION:
TRANSACTION 24058980, ACTIVE 8 sec starting index read
mysql tables in use 1, locked 1
5 lock struct(s), heap size 1184, 2 row lock(s), undo log entries 1
MySQL thread id 357, OS thread handle 0x7faef190e700, query id 76125 192.168.2.127 root updating
update t_user
    set score = score + 10
    where id = 1
*** (2) HOLDS THE LOCK(S):
RECORD LOCKS space id 9890 page no 3 n bits 72 index `PRIMARY` of table `ahamp-cms`.`t_user` trx id 24058980 lock mode S locks rec but not gap
Record lock, heap no 2 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
 0: len 4; hex 80000001; asc     ;;
 1: len 6; hex 0000016f1c5d; asc    o ];;
 2: len 7; hex 75000001481517; asc u   H  ;;
 3: len 4; hex 74657374; asc test;;
 4: len 4; hex 80000037; asc    7;;

*** (2) WAITING FOR THIS LOCK TO BE GRANTED:
RECORD LOCKS space id 9890 page no 3 n bits 72 index `PRIMARY` of table `ahamp-cms`.`t_user` trx id 24058980 lock_mode X locks rec but not gap waiting
Record lock, heap no 2 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
 0: len 4; hex 80000001; asc     ;;
 1: len 6; hex 0000016f1c5d; asc    o ];;
 2: len 7; hex 75000001481517; asc u   H  ;;
 3: len 4; hex 74657374; asc test;;
 4: len 4; hex 80000037; asc    7;;

*** WE ROLL BACK TRANSACTION (2)

as you can see from the log above, thing 1 waits for lock_mode X locks rec but not gap waiting , that is, X lock, and thing 2 holds lock mode S locks rec but not gap , that is, S lock, waiting for X lock.
so how do these two things form a deadlock? First understand what S-lock and X-lock are.

• S lock: a read lock (shared lock) is a lock created by a read operation. Other users can read data concurrently, but no transaction can modify the data (acquire exclusive locks on the data) until all shared locks have been released. If transaction T adds a shared lock to data A, other transactions can only add a shared lock to A, not an exclusive lock. Transactions that are allowed to share locks can only read data and cannot modify it.
• X lock: write lock (exclusive lock) if transaction T adds an exclusive lock to data A, other transactions can no longer add any kind of lock to A. A transaction that is granted an exclusive lock can both read and modify the data.

the order in which locks are acquired in the method under analysis:

insert log (id,xxx) select x where user id = 1 ------ (1)
update user where id = 1 -----------------------------(2)

operation (1) acquires user.id=1 S lock, operation (2) acquires user.id=1 X lock transaction An and transaction B acquire locks in the following order:

------------A------------------------------------------B------------------
----user.id=1S-----------------------------------------------------
--------------------------------------SBuser.id=1S------
--XA-------------------------------------------------
--user.id=1S------------------------------------------------
----------------------------------user.id=1X
-----------------------------------------------------------------
---X-----------------------------------------------------

this is the whole process, and in the end, only part of the transaction commits normally. The title of
can follow aneasystone's blog . His series of blogs are written in more detail.
mysql read / write locks and transactions