Tool Steel includes hard steel alloys that are primarily used in cutting tools. Examples include D2, O1 and the Crucible CPM series, and M4.
Carbon Steel is a low chromium steel often used survival knives and machetes because of its durability, toughness. It holds an edge well and is relatively easy to sharpen but less corrosion resistant due to its low chromium content. Example: 1095.
Stainless Steel is carbon steel with at least 13% chromium content. It is more corrosion resistant but often less toughness. Examples include: 400, 154CM, AUS, VG, CTS, MoV, SxxV, etc.