Not exactly. You do want a deflagration and not a detonation, but "explosion" is more loosely defined and, depending on who you're talking to, a self-sustaining subsonic flame front and a sharp pressure spike are a perfectly valid explosion.
Combustion is a broader term — combustion just refers to burning. And the reason it is called an internal combustion engine is to contrast it from its predecessor combustion engine designs - the external combustion engine.
More precisely, the type of combustion happening in an ICE engine is (low) explosive.