Wiring from garage panel to welder

NEC 630.11(A) may be of interest.

National Electric Code 2008

ARTICLE 630 Electric Welders

II. Arc Welders

630.11 Ampacity of Supply Conductors.

(A) Individual Welders. The ampacity of the supply conductors shall be not less than the I1eff value on the rating plate. Alternatively, if the I1eff is not given, the ampacity of the supply conductors shall not be less than the current value determined by multiplying the rated primary current in amperes given on the welder rating plate by the factor shown in Table 630.11(A) based on the duty cycle of the welder.

Also take a look at 630.12 Overcurrent Protection.

The Owners manual (PDF) seems to contain the answer.

Wiring from service panel to sub panel

If we look at 110.14(C) in 2008 NEC, it says:

National Electrical Code 2008

ARTICLE 110 Requirements for Electrical Installations

I. General

110.14 Electrical Connections.

(C) Temperature Limitations. The temperature rating associated with the ampacity of a conductor shall be selected and coordinated so as not to exceed the lowest temperature rating of any connected termination, conductor, or device. Conductors with temperature ratings higher than specified for terminations shall be permitted to be used for ampacity adjustment, correction, or both.

Which means we'll have to check the breakers temperature rating, and the subpanel terminals temperature rating. Then we'll have to look at table 310.16 (Table 310.15(B)(16) NEC 2011), so we can determine the wire size we should use.

In this example image you can see if we're using copper, we'll use 60°C. Once we look at the table, we'll see that for 50A @ 60°C we need 6 AWG copper wire. (50A @ 75°C = 8 AWG).

110.14(C)(1)(a) basically says that if the temperature is not listed, use 60°C for circuits less than 100A. 110.14(C)(1)(b) says if the temperature is not listed, use 75°C for circuits over 100A. However, in the real world 75°C is often used for both.

You don't have to do anything to identify the conductors. However, you'll have to worry about box fill, as these conductors will have to be counted in the fill calculation.

National Electrical Code 2014

Chapter 3 Wiring Methods

Article 314 Outlet, Device, Pull, and Junction Boxes; Conduit Bodies; Fittings, and Handhole Enclosures

314.16 Number of Conductors in Outlet, Device, and Junction Boxes, and Conduit Bodies.

(B) Box Fill Calculations.

(1) Conductor Fill. Each conductor that originates outside the box and terminates or is spliced within the box shall be counted once, and each conductor that passes through the box without splice or termination shall be counted once. Each loop or coil of unbroken conductor not less than twice the minimum length required for free conductors in 300.14 shall be counted twice. The conductor fill shall be calculated using Table 314.16(B). A conductor, no part of which leaves the box, shall not be counted.