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Is there a different meaning to the word of 'parameter' in engineering? I've started in engineering from a mathematics/physics background, and commonly a 'parameter' is either used to 'parameterize' a curve with a vector-valued function, or to define a set of functions/to generalize a type of system where certain properties can define a slightly different specific system or scenario (an object with constant mass but 'm' is unspecified) however I've heard more generally 'time' or 'position' be described as 'parameters' is this common engineering language, in which case should I avoid the other two uses of the word, and what would be a word to describe the second case would it simply be 'constant'? I don't like this word as in some contexts, a 'constant' has to be a symbol that represents a particular number, and not something which is being left general.

user1007028
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Parameter just means something that can be quantized in engineering. Basically a synonym for variable. Honestly, I don't see it used any differently in math and physics so I am not sure where you are coming from. I have no idea why you don't consider time or position parameters. Also, parameters can be "fixed" which means you do not get to choose what that value is in your design due to context. This is not quite the same as being constant.

Some interpretations of "parameters" in math and physics might only refer to inputs, not outputs. In physics and math you have data that you put into your model and you get your prediction. You don't get to choose your outcome and then work backwards to get your data.

But in engineering you are designing towards a known end goal so you need to be able to choose what that end goal is. In other words, you get to choose what your final result will be. So in a sense, you get to choose both inputs and outputs in engineering. Whether you can actually make something that satisfies them is another story.

But if you just call something an output parameter you are back at the definition at the very top.

DKNguyen
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Adding to DKNguyen, One interesting aspect of this question is that etymology of the word "parameter". It literally means something that is beside the meter/measure.

So it is:

a quantity or process that affects the measure or the outcome, and that its influence cannot be neglected (thus needs to be mentioned with the measure/outcome)

E.g. if you are measuring the strength of a alloy you need to report if any heat treatments took place. The heat treatments are parameters.

Bottom line is that the words parameter and variable can --IMHO-- be used interchangeably. Apart from that, I consider variable to apply to countable quantities and inputs, while parameter can be more general and apply to quantities and processes and also outputs (e.g. application of heat treatment or not)

NMech
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Annex A to the ISO 80000-1:2013 standard encodes some relevant thoughts. In general,

If no special name for a quantity exists, a name is commonly formed in combination with terms like coefficient,factor, parameter, ratio, constant, etc.

In particular,

Combinations of quantities which occur as such in equations are often considered to constitute new quantities. Such quantities are sometimes called parameters.

EXAMPLE Grüneisen parameter: $\gamma\qquad\gamma = \alpha_V/\left(kc_V\rho\right)$

However,

It is not the intention of this annex to impose strict rules to eliminate the relatively frequent deviations which have been incorporated in the various scientific languages.