I bought a new in-wall timer rated 20 Amps. and it says '1350 w Tungsten', so I'm wondering if there are watts which are measured different then other watts? In my calculation it should be 20 x 120 = 2400.
Yes, apparently "tungsten-heater" load type is measured differently than a ideal/purely resistive load type!
Check this for example - http://www.nkkswitches.com/pdf/electricalratings.pdf - you will see chart of the current v time "inrush" curve for tungsten filament electrical light bulbs - while cold, their resistance is very low - so they spike when switched on (not coincidently that's the time when these burn out - during power-on).
And thus differences in ratings, for example this smart switch allows only 1/2 tungsten load than resistive:
ELECTRICAL RATINGS • Electrical rating: 15A, 120Vac, 60Hz • Resistive: 1800W • Tungsten: 960W • Electrical Ballast: 500VA • Type 1.B Action
Different devices have different characteristics when the timer breaks the circuit.
They usually rate the contacts of the timer by resistive (tungsten) or inductive (motor) style loads.
Even though the contacts are rated for 20 amps a resistive load may be more likely to pit the contacts so they derate the timer for a resistive load.
EDIT - The particular timer you have is only rated for a 1 HP motor which translated to 746 watts and 6.2 amps of inductive load. 1350 watts of Tungsten resistive load which translates to 11.25 amps of standard lighting. Even though the specs say it has 20 amp contacts it is not rated to switch a 20 amp load. Apparently over-promising and under-delivering. 😞