There are several different functions that can be called in Postgres to get the current date and time. 

SELECT CURRENT_TIMESTAMP as CURRENT_TIMESTAMP, 
    TRANSACTION_TIMESTAMP() as TRANSACTION_TIMESTAMP,  
    LOCALTIMESTAMP as LOCALTIMESTAMP, 
    NOW() as now, 
    CLOCK_TIMESTAMP() as CLOCK_TIMESTAMP;

current_timestamp = 2023-02-01 14:04:17.388 -0500
transaction_timestamp = 2023-02-01 14:04:17.388 -0500
localtimestamp = 2023-02-01 14:04:17.388
now = 2023-02-01 14:04:17.388 -0500
clock_timestamp = 2023-02-01 14:04:17.388 -0500

Calling all of these functions return the same information, except that LOCALTIMESTAMP returns the datetime without the time zone offset (I’m in the Eastern United States, currently 5 hours behind UTC).

CURRENT_TIMESTAMP is a SQL standard function, where TRANSACTION_TIMESTAMP and NOW are Postgres functions. NOW is certainly easier to remember, where the TRANSACTION_TIMESTAMP may be a little clearer that it is the same value to be used for multiple calls in a transaction.

All of the functions will return the same value, no matter how many times they are called within a transaction, except for CLOCK_TIMESTAMP. It will return the datetime at the time the function is called. It’s a little clearer when we call the functions twice, with a delay in between.

DO $$
DECLARE v_dummy text;

BEGIN
	
RAISE NOTICE '1st Calls';
RAISE NOTICE 'CURRENT_TIMESTAMP = %', CURRENT_TIMESTAMP;
RAISE NOTICE 'CLOCK_TIMESTAMP = %', CLOCK_TIMESTAMP();

-- Delay for one second
SELECT INTO v_dummy pg_sleep(1);

RAISE NOTICE '';
RAISE NOTICE '2nd Calls';
RAISE NOTICE 'CURRENT_TIMESTAMP = %', CURRENT_TIMESTAMP;
RAISE NOTICE 'CLOCK_TIMESTAMP = %', CLOCK_TIMESTAMP();

END $$;

Results:
1st Calls
CURRENT_TIMESTAMP = 2023-02-01 14:15:28.878426-05
CLOCK_TIMESTAMP = 2023-02-01 14:15:28.92468-05

2nd Calls
CURRENT_TIMESTAMP = 2023-02-01 14:15:28.878426-05
CLOCK_TIMESTAMP = 2023-02-01 14:15:29.955542-05

There are also CURRENT_DATE and CURRENT_TIME functions to return the date and the time portion of CURRENT_TIMESTAMP.

Links:
Postgres – Datetime Functions
Database Guide – transaction_timestamp