You're on the right track, but it's not necessarily that. That 'showing' sentence was just a more elaborating and descriptive version of the 'telling' sentence, but "steadily" is beginning to establish something about the character. Showing instead of telling comes from taking an emotion or sensation and expressing it in a physical movement. Most of the time, it comes from drawing out sentences that tell so that it gives an action that furthers the plot, but also establishes characterisation and possibly setting, among other aspects of fiction. There's a great chapter on showing and not telling in Stein on Writing, segments which I'll post here (some sections paraphrased):
Telling: He was nervous.
Showing: He tapped his fingers on the tabletop.
Telling: She boiled water.
Beginning to show: She put the kettle on the stove.
Showing: She filled the kettle from the faucet and hummed till the kettle’s whistle cut her humming short.
Showing: She boiled water in a lidless pot so she could watch the bubbles perk and dance.
Telling: He took a walk.
Beginning to show: He walked four blocks.
Showing more clearly: He walked the four blocks slowly.
Showing more: He walked the four blocks as if it were the last mile (this gives the reader a sense of the character’s feelings, which the previous version did not.)
Shows the most: He walked as if against an unseen wind, hoping someone would stop him (gives the reader a sense of what the character desperately wants.)
"If you are concerned about whether in any passage or chapter you are telling rather than showing, there are some questions you can ask yourself:
Are you allowing the reader to see what’s going on?
Is the author talking at any point? Can you silence the author by using an action to help the reader understand what a character feels?
Are you naming emotions instead of conveying them by actions? Is any character telling another what that character already knows?"
Hope I can be of help.
