Should my Ottawa quote say dampproofing or waterproofing in writing?

Your quote should name exactly which protection is being applied, because Ontario's Building Code treats dampproofing and waterproofing as two different requirements with different conditions.

What the Code says

Dampproofing (clause 9.13.2) is required on the exterior of foundation walls below grade where the finished ground outside is higher than the ground level inside. Waterproofing (clause 9.13.3) is required where hydrostatic pressure occurs. The Code gives no number or test for when hydrostatic pressure occurs, and it does not say every basement needs waterproofing. The choice turns on whether hydrostatic pressure is present at your foundation, and that is something the contractor assesses at the house, not something this site can determine for you.

The practical difference matters for your quote because the two systems are not interchangeable. Dampproofing is not required where the wall is waterproofed, but the Code does not allow dampproofing to substitute for waterproofing where hydrostatic pressure exists. If a contractor proposes dampproofing, ask them to explain in writing why hydrostatic pressure is not a factor at your foundation. If they propose waterproofing, ask them to confirm the membrane is continuous across joints and at wall-to-footing junctions, as clause 9.13.3 requires.

A few other things worth checking in the written quote:

• whether the foundation wall is poured concrete or block, because block walls require at least 6 mm of mortar parging on the exterior face below grade before any dampproofing or waterproofing is applied (clauses 9.13.2.3 and 9.13.3.3)
• whether drain tile is being replaced or left in place, and where it discharges
• whether the membrane is protected from damage during backfilling, as clause 9.13.3.4 requires

Published Ontario contractor pricing for exterior work that includes excavation, a membrane, drainage and new tile runs roughly $100 to $350 per linear foot of wall, with deeper foundations and tight access pushing the figure higher. If your quote is for dampproofing only, too few published figures exist for that alone to give a useful range.

Read the quote line by line and ask the contractor to point to the specific word, dampproofing or waterproofing, and to explain in plain language which clause of Ontario's Building Code their proposed system satisfies.