In our example experiment, our response (dependent) variable "plant height after 14 days" is a continuous numeric variable. Additional examples of continuous numeric variables are temperature, weight, time, or distance. If instead (or in addition) we had decided to measure the number of leaves on each plant after 14 days, then this would be a discrete numeric variable, as it can only take on discrete values. Another example of a discrete numeric variable would be "number of hairs on the thorax" of a fly, or number of petals on a flower.
Perhaps the species of plant we opted to use in our experiment can produce different colours of flower on different plants. If this is something we planned to measure, then the "flower colour" (red, pink, white) produced by each plant would be an example of a nominal categorical variable. Another example of a nominal categorical variable would be "birth country", or "hair colour". Lastly, if we had planned to judge the "odour strength" of the flowers, we might have scored odours as "weak", "moderate", and "strong", which constitutes an ordinal categorical variable, because the categories have a logical order to them.
But what about our independent variable? In our example experiment, temperature is the independent variable, and let's say we subjected the plants to three different temperatures: 10, 20 (control), and 30 degrees Celsius. Strictly speaking, temperature is another example of a continuous numeric variable. However, in our experiment we are manipulating the temperature to be exactly 10, 20, or 30 degrees Celsius. Thus, our independent variable can be considered a discrete numeric variable, or in practice, it could also be treated as an ordinal categorical variable (either approach would be ok). In human health research, experimental studies often test the effects of different drugs on some health outcome, in which case "drug type" would be an example of a nominal categorical independent variable.