What name could be used in building code for "interior drain tiles"?
The code seems to use the term &quot;subsurface soil drainage&quot;, but I wasn't able to find any detail on subsurface drainage.

§ 18-29-712.3.2
Sump pit.
The sump pit shall be not less than 18 inches (457 mm) in diameter and 30 inches (762 mm) deep, unless otherwise approved. The pit shall be accessible and located such that all drainage flows into the pit by gravity. An approved sump pit or tank within a building receiving the discharge from sanitary drains, storm water or combined drains shall be constructed of steel, cast iron, reinforced concrete pipe or other approved materials. The sump or tank receiving the discharge from subsurface soil drainage shall be constructed of vitrified clay tile or any of the above materials. Approved plastic or fiberglass liners may be used in conjunction with any of the approved materials referenced above. The pit bottom shall be solid and provide permanent support for the pump. The sump pit shall be fitted with a gas-tight removable cover adequate to support anticipated loads in the area of use. The sump pit receiving sanitary flow shall be vented in accordance with Article 18-29-9.

I also searched for vitrified clay tile, but didn't come up with much.
I'm not sure how useful it is, but International Residential Code (IRC) has this to say.

International Residential Code 2012
Chapter 4 Foundations
Section R405 Foundation Drainage
R405.1 Concrete or masonry foundations.
Drains shall be provided around all concrete or masonry foundations that retain earth and enclose habitable or usable spaces located below grade. Drainage tiles, gravel or crushed stone drains, perforated pipe or other approved systems or materials shall be installed at or below the area to be protected and shall discharge by gravity or mechanical means into an approved drainage system. Gravel or crushed stone drains shall extend at least 1 foot (305 mm) beyond the outside edge of the footing and 6 inches (152 mm) above the top of the footing and be covered with an approved filter membrane material. The top of open joints of drain tiles shall be protected with strips of building paper. Perforated drains shall be surrounded with an approved filter membrane or the filter membrane shall cover the washed gravel or crushed rock covering the drain. Drainage tiles or perforated pipe shall be placed on a minimum of 2 inches (51 mm) of washed gravel or crushed rock at least one sieve size larger than the tile joint opening or perforation and covered with not less than 6 inches (152 mm) of the same material.
Exception: A drainage system is not required when the foundation is installed on well-drained ground or sand-gravel mixture soils according to the Unified Soil Classification System, Group I Soils, as detailed in Table R405.1.
R405.1.1 Precast concrete foundation.
Precast concrete walls that retain earth and enclose habitable or useable space located below-grade that rest on crushed stone footings shall have a perforated drainage pipe installed below the base of the wall on either the interior or exterior side of the wall, at least one foot (305 mm) beyond the edge of the wall. If the exterior drainage pipe is used, an approved filter membrane material shall cover the pipe. The drainage system shall discharge into an approved sewer system or to daylight.

I've found that most building departments are quite helpful, and enthusiastically provide information to inquisitive homeowners.  Your best bet might be to contact your local building department, and see what information they can provide.