That html link is correct for what it says, but is a bit misleading: "Round Tube steel" IS a structural member of specific material properties and tight shape tolerances OFTEN (not always) not met by "pipe" - round steel or stainless members intended to transport liquids and powders. This is because "round structural steel members rarely face internal pressures, but are frequently faced with bending stresses and column-like compression stresses that become exaggerated when the structural member is trying to resist failure affected by geometry (out-of-roundness) or out-of-straightness.
"Pipes" on the other hand, when faced with internal pressure, will actually tend to straighten and go "back into round" as they deflect.
However, "tubes" also are selected for fluid services for specific purposes, but ARE always designated by their OD as in the html linked page. Heat exchangers, for example, will use "tubing" instead of "pipe", and small instrument lines are usually tubing (1/4 dia stainless tubing, 1/2 inch dia tubing used in a drain line or bleed line, for example)
Pipe manufacture and properties are governed by completely different specifications than tubing. Application and product form will determine which applicable ASME/ASTM spec to use. For example, 2-1/4 Cr 1 Mo high temperature boiler tubing is specified as ASME SA 213 Grade T22 while piping is specified as ASME SA 335 Grade P22.
Short version:
Pipe, specified by nominal sizes (not actual dimensions) with fairly loose tolerance.
Tube, specified by actual size (usually OD and wall) with tight tolerances.
You also fine many custom tube products, special sizes, tolerances, finishes, and strengths.
The productions and testing methods are defined by the actual specifications and are often the same for pipe and tube, though many tubing specs do require must stricter NDT of the final product.
As mentioned above, the most importance is the purpose.
Pipe : mass transfer(The size can be larger to sustain the effective mass transfer.)
Tube : heat transfer(The size should be smaller to sustain the effective heat transfer.)
For instance, fired heater tubes (e..g, API 530/560) are normally using pipe materials, but we call them HEATER TUBES instead of heater pipes because the main purpose is heat transfer.
The next will be the followings (other than above answers).
