In Resident Evil 2 the game is automatically saved at difficulty levels Assistance and Standard after completing each key storyline stage and before the boss battles. On the Hardcore difficulty, the automatic save function is deactivated. The same features also apply to "2nd Run".
In the game, you can save the state of the game manually. To do this, find a typewriter. The number of record states per game is not limited.
The exception is the Hardcore mode again: to save the game in this mode, in addition to finding the typewriter, you must also have some ink ribbon. It can be found in places where other items, e.g. weapon magazines, occur at lower difficulty levels. As a result, there are fewer items to collect in the Hardcore mode; in addition, ribbons take up space in your inventory (so it's worth keeping them in black boxes).