I am absolutely surprised that not one person has mentioned to have marklobo review ASME B16.34 and ASME/ASTM SA/A 350. Using the example cited in the OP, I can see why marklobo has asked the question.
ASTM A 350 LF2 is listed in ASME B16.34 Table 1 as supplied in two product forms - forging and bar. The key words are "product form" in this Standard. A forging is a product form, and bar is a product form that can be machined into a final product form, but it is NOT a forging product form.
At this point, one has to go back and review the specific material specification, in this case it is ASTM/ASME A/SA 350.
As stated in Scope 1.1, This specification covers forged flanges, ring rolled flanges, forged valves and fittings...
(note the following)....Although this specification covers some piping components machined from rolled bar and seamless tubular products (see 4.3.3), it does not cover raw material produced in these product forms.
Following the reference cited to 4.3.3 in SA 350 it so states,
4.3.3 Except for flanges of all types, hollow cylindrically shaped parts may be machined from rolled bar or seamless tubular products provided that the axial length of the part is approximately parallel to the metal flow lines of the stock. Other parts, excluding flanges, may be machined from hot rolled or forged bar through and including NPS 4.
So, as defined in the Scope of ASME SA 350, forged valves are specifically mentioned or singled out as a product form and, as such, does not imply that product forms can be machined from forged bar and be called forgings.
Thus, forged valves cannot be supplied as forgings from machined, forged bar.