If the hiding of emotions was not intentional, then it could be a flat affect. That is admittedly two words, but it's the term I've been diagnosed with. It can be associated with schizophrenia, depression, brain damage, or autism (I have the latter). On rare occasion, it can be present absent other factors.
Someone who is stoic doesn't necessarily hide all of their emotions; stoicism is more about persevering without complaint, not particularly seeking pleasure, and taking life as it comes. Someone who holds to the Stoic philosophy strives to lack joy or grief, rather than just not show it.
Someone who is diffident lacks self-confidence, according to the dictionary definition of the word.
Someone who is self-composed chooses whether or not to express their emotion. It could be due to a flat affect or it could be from training. It's my understanding there is a connotation of the latter, however. In any event, the self-composed individual knows how to portray the emotions that aren't being shown.
Someone who has a practiced facade is very definitely doing it deliberately, and they've spent time making sure they get it right.
I believe impassive and self-composed are similar, but it feels to me like impassive seems stronger - that someone who is self-composed seems more likely to be able to be goaded into an emotional display than someone who is impassive. It's also not as clear that the impassive person knows how to show the emotion they're feeling, or that they are feeling.
Someone who is reserved is generally self-composed, in my experience. Some of the people I've known who were described as reserved had a blunted affect, which is similar to a flat affect, but not as pronounced. If a person has a blunted affect, and they're not controlling their emotional display, they will display emotion, but if you're not looking for it, you might miss it. More likely, you'll just think they're a lot less enthusiastic about something than they are.
Someone who is expressionless is similar to someone who is impassive, but there seems to me to be less of a connotation of apathy. But unlike someone with a flat affect it doesn't feel to me like there's a definite connotation of having emotion; the situation is just unclear.
Other affect terms are broad affect, which is what normal people have, restricted affect and constricted affect, which is between broad and blunted, and labile affect means their emotional display is really variable.
Technically speaking, it's possible to have a combination of different affects - for some emotions, the person just doesn't have a natural reaction at all. For others, they have a natural reaction, but it's less distinct than normal yet not as muted as a flat affect is - for example, they may tend to not show much joy, unless they're consciously trying. However, even when not paying attention to their presentation, when they're happy they will at least smile. A bit. But surprise or anger just don't get reflected in their outward appearance without an effort. It doesn't mean it's not real. But if it is real, there's going to be at least a second or two of pause between the surprise and the act.
That having been said, in my limited experience, ones startle response is not an emotion. That's a purely physical self-preservation thing, and whether it's a strong response or not really doesn't seem to be affected much by their affect. Not everyone with a flat affect will necessarily have a normal startle response, but everyone I know with that diagnosis at least startles to a normal degree. But then after the startle, there will be a pause, while the person figures out what emotion to show, because whatever emotion it is, their affect isn't going to portray it right on its own.