In Chapter 16 of HMC there is a vivid and exciting set-piece in which Howl and the Witch of the Waste engage in a full-out no-holds-barred magical duel that in its violence and power scares the daylights out of everybody for miles around. For reasons that we later learn, the two are so evenly matched it’s impossible to tell which fanged monstrous illusion is which, and at the end of it not even Howl is certain who won. 
The Witch of the Waste is not the only sorceress/witch against whom Howl’s powers are tested (I count six in all). From the moment he enters his castle on the 9th of May to find that Sophie has “bullied” Calcifer into letting her cook on him, the two of them lock horns, enter the crucible, and are pitted against — and for — one another for keeps. (Have I missed any clichéd metaphors?) Even funnier, neither of them can figure out what the hell is going on.
First off, Sophie recognizes Howl at once as the young man she saw on May Day. He seemed so kind and concerned then, even though she was mortified by his pity and her own panic. To think that if she’d gone off with him he might have made mincemeat of her! Not that she’s so far found any evidence in his castle of mincemeated young girls, despite getting some heavy-duty snooping in before breakfast.
Howl recognizes her too, though not with the same clarity with which she can see him. He’s a little less dandified than he was on May Day, but he’s made no radical change in either his appearance or his outfit.
Sophie, on the other hand, has been altered and aged by not one but two (per Calcifer on p. 44) heavy-duty spells. And she’s a powerful spell-caster herself, as we have seen from the results she got from talking to hats!
“Who on earth are you?” said Howl. “Where have I seen you before?”
“I am a total stranger,” Sophie lied firmly. 
A masterful line of dialogue, that — an absolute give-away that she’s NOT a total stranger, and yet it’s Sophie saying it, and whatever Sophie says, IS. It comes true. She’s just offered Howl a lame evasion and a confounding spell all in one helping. The irony meter in his brain must be over the red line. If he weren’t running for his life from the Witch of the Waste, he might be delighted and intrigued by it all. As it is, however…
As it is, Sophie is emphatic in her determination that he is NOT going to know that she is the girl he pitied on May Day. Are her thoughts powerful enough to cast Howl into further confusion, even if she hasn’t spoken this particular one aloud? Hearts and souls have nothing to do with it, she vows inwardly. He can eat my heart, he can steal my soul, he can go full-metal Bluebeard on me, but he is NOT going to know that I was that poor pitiful mouse of a girl. If only things had gone better on May Day! And yet, and yet, he’s turned out to be none other than Wizard Howl. It’s possible that Sophie is concealing from herself the very real heart-ache and crushing disappointment she must be feeling.
Because, you see, hearts and souls have got EVERYTHING to with it.