There is no difference ! The counter adds up external events. The timer adds up internal events, derived from the crystal.

You are exactly on track with everything else. You can usually use your assembler like this though:

MOV TH0,#HI(15536)
MOV TL0,#LO(15536)

Your version may be different, it could be HIGH and LOW

TO count one minute, you have to count 60 1 seconds. Get that working, then look at using the TIMER interrupts to do the work for you.

You are getting there Waqar, well done.
Steve