What is different between a B737 and B757?
Although the 737 has grown over the years, the 737 and 757 remain in different size classes. Both models can be ETOPS certified, although the 757 is more often used in long flights.

At the time the 757 was introduced (in the 80's), the 737 classic series was current. For the 737-400:

Passengers: 146
Length: 119 feet
Wingspan: 95 feet
Wing area: 1135 sq feet
MTOW: 138,000 lb
Takeoff distance: 8000 feet
Range: 2160 nm
Thrust: 2x 23,500 lbf
Max fuel: 5,311 US gal

The 757 was significantly larger. For the 757-200:

Passengers: 200
Length: 155 feet
Wingspan: 125 feet
Wing area: 1951 sq feet
MTOW: 255,000 lb
Takeoff distance: 6500 feet
Range: 4100 nm
Thrust: 2x 43,500 lbf
Max fuel: 11,489 US gal

The 757 is about 35 feet longer, seats about 50 more passengers, and flies about 2,000 nm further (roughly twice as far). The extra range is due to the larger wingspan and longer fuselage, being able to carry more fuel. For this reason, the 757 is used on longer and busier routes, while the 737 is used on shorter, less busy routes.

In the 90's, both models were updated. The 737 was significantly upgraded, including new wings and a new engine, which increased its efficiency. The 737 NG series eventually included the 737-900ER model, currently the largest 737 model.

Passengers: 180
Length: 138 feet
Wingspan: 117 feet
Wing area: 1341 sq feet
MTOW: 187,700 lb
Takeoff distance: 9843 feet
Range: 3235 nm
Thrust: 2x 28,400 lbf
Max fuel: 7,837 US gal

The 757-300 was also introduced. This was a stretched version of the 757-200.

Passengers: 243
Length: 178 feet
Wingspan: 125 feet
Wing area: 1951 sq feet
MTOW: 272,500 lb
Takeoff distance: 7800 feet
Range: 3595 nm
Thrust: 2x 43,500 lb
Max fuel: 11,489 US gal

Although the more efficiency gains of the new 737 bring the range up to nearly that of the 757, the 757 remains significantly larger.