Pastel Punk is a term used to describe the style of stereotypical punk things (chains, spikes, combat boots, etc.) but in, or combined with, soft pastel colours. They often dye their hair like regular punks as well, but opt for more pastel shades than electric dyes.
Pastel Punks often don't behave like other punks, having more of a love for aesthetics and clothing than a 'fuck society, let's all stand up against the government' attitude. They're essentially the softer version of punk.
Pastel Punk is incredibly similar to Pastel Goth, they both take the original style and add more pastel colors to it to match what they feel comfortable in. They may also have slightly different music taste due to their softer nature.