Your engine was made on 15 August 1975. Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6jmvGVJ1DajI.pdf

Here is the Operator's Manual:
http://bsintek.basco.com/BriggsDocumentDisplay/lrvvA-wU7eL7hAxB91ObQ.pdf

Your engine's model number, 80102, tells you quite a bit about it. The first digit tells you it has a displacement of 8 cubic inches (130 cc). The second digit says it is of the very first design generation after Briggs adopted its standard model numbering system. The third digit means it has a horizontal crankshaft and a Vacu-Jet carburetor. The fourth digit signifies that it has plain main bearings, not ballraces, and it does not have a flange mount, or gear reduction, or any form of auxiliary drive. The fifth digit says it has a rewind starter.

For your immediate purposes the key point is that it had when it was new, a Vacu-Jet carburetor, not the more elaborate Pulsa-Jet. However your picture shows that it now has a Pulsa-Jet. (Note that it still has the Choke-A-Matic coupled choke, which was available with both carburetors). That means somewhere along the line, someone has converted your 80102 into an 80202, as far as carburetor and fuel tank are concerned. In case you care, the simple way to distinguish between Vacu-Jet and Pulsa-Jet on that generation of carburetors, is that the pull-knob on the choke is horizontal on the Vacu-Jet and vertical on the Pulsa-Jet.

The Pulsa-Jet has a built-in fuel pump, while the Vacu-Jet relies purely on venturi vacuum to draw fuel up from the fuel tank. The Vacu-Jet was not really satisfactory with the deep fuel tank which your engine has - the Pulsa-Jet does not let the mixture lean out when the fuel level in the tank is low. Presumably someone switched the tank and carburetor as an assembly, so as to make a shallow-tank engine into a deep-tank engine. I believe that model mower was, over time, fitted with all combinations of carburetor and fuel tank.

Getting down to minor points, being made prior to 1982, your engine had a breaker-point ignition system when it was new. It is commonplace for people to convert those engines to electronic (Magnetron) ignition, though, if the breaker-point system gives trouble. Generally it is easier to do that than to replace the points or condenser, and it makes the system more durable. You would have to remove the cooling air cowl to find out whether it has been done to your engine.