Yes, they are similar in many ways, but different enough to require different skill sets.
is more physically active and "can" require math/trig/geometry to calculate stairs and loads for structures ... roughly. Measuring and calculating are very important, but especially here. Cutting the materials, 2 X's and sheet goods can be only slightly less accurate, sometimes even very precise, so the machine and tool need to be top grade.
may require more carving and shaping depending on the different styles. Mission Style uses very little hand carving in the basic joinery, but for mortises and tenon and dovetails carving is needed. The dimensioning of rough lumber requires different skills and machines than cabinetry or carpentry where construction sizes are used most of the time. You won't be reducing the thickness of plywood as a rule.
uses sheet material in large sizes and broken down accurately into smaller panels. Frames and supports are made from hardwood in various smaller sizes as well.
Basic joinery methods comes to bear in all 3 areas, so get familiar with the common joints, where they are used and why. Fasteners are different in the 3 areas also. Furniture is often made without any mechanical fasteners.
Gluing up materials for cabinets and large doors and tables is a valuable skill and requires many sizes of clamps and braces. You can't have too many clamps, and if you do, you won't on the next project.
Patience is a skill that is required here!
NOW, if you decide which area of woodworking you like or suits you best you can concentrate on acquiring those machines and skill sets.
Some schools offer apprenticeships in various trades but they are becoming harder to find locally.