In the series, you will find a variety of stainless steel grades that help describe the specific properties of the alloy, such as toughness, magnetic properties, corrosion resistance and alloy composition.
Older grades typically have three-digit identifiers established by the Society of Automotive Engineers (SAE).
However, you may also see grades in North America identified using a six-character identifier set by the American Society for Testing and Materials (ASTM).
These are called Unified Numbering System (UNS) identifiers. You can find a full list of commonly used identifiers here.
In many cases, UNS identifiers share the same first three digits as their AISI identifiers.

But there are also scoring systems created by:
British Standard (BS)
International Organization for Standardization (ISO)
Japanese Industrial Standards (JIS)
European standard
German Standard (DIN)
Chinese standard (national standard)
Due to the large number of different standards and grading systems, it can be difficult to obtain a great deal of information about the unique composition of a given alloy from its grade.

For example, SAE Standard 304 stainless steel may also be graded as:
EN number: 1.4305
CN name: X8CrNiN18-9
USA: S30400
DIN: X5CrNi18-9, X5CrNi18-10, X5CrNi19-9
BS: 304S 15, 304S 16, 304S 18, 304S 25, En58E
JIS: SUS 304, SUS 304-CSP
However, to receive a given grade designation, the alloy must adhere to strict requirements set by the organization that maintains the standard.

In the case of general SAE standards, 304 stainless steel must contain:
18% to 20% Chromium
8% to 10.5% Nickel
0.08% carbon
2% manganese
0.75% Silicon
0.045% Phosphorus
0.03% Sulfur
0.1% nitrogen
Every addition or adjustment of alloy composition affects every aspect of stainless steel performance.

If you're not sure about the exact grade of steel you need, or what the compositional requirements for the various grades are, the list linked below provides a breakdown of the most common options:

SAE and UNS chemical composition and mechanical properties
BS EN Stainless Steel Composition
MatWeb Metal Alloy UNS Number Search