When a manufacturer specifies tempco for a precision resistor or trimpot (eg +- 10 ppm/C ) - does that represent the expected range across different component samples?
This specification means that for a given component, the TC can be anywhere within the range given, this does not mean that the TC of the component will vary between + and - 10 PPM/°C (for your example) over its operating range. The TC 'curve' can be linear or nonlinear with temperature, in many cases it is nonlinear, it will change some within its operating temperature range. This characteristic depends on the material used in the component, for resistors there are quite a few different types of elements made from metal alloys and so-called plastic elements such as the cermet types. The method of manufacture will also affect the TC 'curve', in their 'raw' form (this is before they are made into a component), the TC tends to be of a fixed characteristic, alloys such as Evanohm will have a fixed TCR that does not vary with normal use. The manufacturing process of the component can affect the 'finished' TC in various ways, stress applied to the resistive element will cause the TCR to 'appear' to change but the actual TCR of the element does not change itself, stress causes change in the resistance which at the terminals appears to be TCR but it isn't and stress is usually a nonlinear function.
A cermet trimmer always has a +/- TCR range, it can be either + or - and the TCR tends to be less than linear, typical cermet trimmers have a TCR of +/- 200 PPM/°C (as an example) meaning that the actual TCR of the trimmer in your hand can be anywhere within that range (-25, +50, -100, +150, -200, ect.) but they will all have a similar TCR 'curve'. Wire wound trimmers generally have the lowest TCR and the most linear TC of all trimmer types but there are wide variances within the various trimmers available. There is only one WW trimmer on the market which has very low and stable characteristics and is military qualified, it is made by Bourns and costs around $10 each, this one has the best long term stability of any trimmer on the market.
Virtually all passive components have TCs and few have linear curves over temperature.
Data sheets may show a TC 'curve' with temperature, this will tell you if the TC is linear or not, linear TC can be compensated for relatively easily, non-linear not so easily. Some resistors will have a low TCR but very non-linear, in some cases, the 'curve' is quite lumpy and varies up and down with temperature, others are hyperbolic, ellipsoid or linear. In some cases, a PWW resistor can have different TCRs above and below the reference temperature, I have one or two spools of wire like that. All of the newer wire I have are single TCR over temperature, in effect linear. Most PWW manufacturers have non-linear TCR curves with increasing TCR at the temperature extremes. In general stress cannot be completely removed although with time it tends to slowly decrease.
Be careful of PPM measurements made with DVMs and ADCs, they can affect the actual readings in unexpected ways unlike a resistance bridge which essentially measures at a null point with extremely high impedance, DVMs and ADC converters do not have that advantage and also have active circuitry at their inputs which can affect the readings. They can produce a non-linear (parallel) error into the readings, it is generally small but an error just the same. While I use DVMs, for critical high accuracy readings a resistance bridge is the only accepted method.