in 1985 these were the following 2.0L engines available form toyota:
21R (1972cc)
2S (1995cc)
3S (1998cc)
3Y (1998cc)
M (1988cc)
2C (1974cc - Diesel)
i'm guessing you have either got a 3S or 3Y as they are both 1998cc (as you mentioned)
3S
3S-FC 87-91 86.0 mm 86.0 mm 9.8:1 1998 cc 85 kW@5600 rpm 166 Nm@4400 rpm Equipped with catalytic converter, was available only in third-world markets
3S-FE 87-90 86.0 mm 86.0 mm 9.8:1 1998 cc 90 kW@5600 rpm 169 Nm@4400 rpm -SS1 (ST202)
3S-FE 87-94 86.0 mm 86.0 mm 9.8:1 1998 cc 85 kW@5600 rpm 162 Nm@4400 rpm Equipped with catalytic converter
3S-FE 95-98 86.0 mm 86.0 mm 9.8:1 1998 cc 96 kW@6000 rpm 178 Nm@4400 rpm Refined valve timing and ECU settings, introduced with Carina E (T19) model
3S-FE 1998-2000 86.0 mm 86.0 mm 9.8:1 1998 cc 94 kW@6000 rpm 178 Nm@4400 rpm Slightly less power with better torque characteristics. Stricter pollution control. Introduced with the new Avensis (T22) model
3S-FSE 2001-2003(?) 86.0 mm 86.0 mm 9.8:1 1998 cc 110 kW@6000 rpm 192 Nm@4000 rpm D-4 (Direct injection), VVT-i (only available in EU/Japan markets?)
3S-GE 85-89 86.0 mm 86.0 mm 9.2:1 1998 cc 103 kW@6200 rpm 175 Nm@4800 rpm Celica 2.0 GT-i 16, GT-R (ST162)
3S-GE late-89-93 86.0 mm 86.0 mm 10.0:1 1998 cc 115 kW@6600 rpm 186 Nm@4800 rpm Celica 2.0 GT-i 16, GT-R (ST182/ST183), MR2 (SW20)
3S-GE 94-99 86.0 mm 86.0 mm 10.0:1 1998 cc 137 kW@7000 rpm 192 Nm@4800 rpm Celica GT, SS-II (ST202), MR2 (SW20)
3S-GE 1999- 86.0 mm 86.0 mm 10.0:1 1998 cc 150 kW @ 7000 rpm 191 Nm @ 4800 rpm MR2 (SW20)
3S-GTE 86-89 86.0 mm 86.0 mm 8.5:1 1998 cc 136 kW (182 hp) @6000 rpm 250 Nm (184 ft