Compare and contrast thunderstorms and blizzards.

At the most basic level, thunderstorms and blizzards are specific weather phenomena that occur most frequently within particular seasonal climatic conditions. Thunderstorms are more common during spring and summer afternoons, whereas blizzards notably require freezing weather conditions (so, basically, wintertime).
Perhaps the most evident difference between thunderstorms and blizzards is the absence of lightning in the latter. In general, you’re not going to hear thunder unless there’s lightning, because it takes a rapid increase in temperature and air pressure from a lightning event to produce the shock wave we associate with thunder. Rarely, you will have thunder within snowstorm conditions, and when this occurs, we call it thundersnow.
Sources for thundersnow include: (a) thunderstorms coming in contact with cold or warm fronts in a winter environment, (b) synoptic snowstorms which mix wintery and precipitous conditions, and (c) lakes and/or oceans come into contact with thunderstorms, which rapidly cool the air across warm waters. We tend not to hear as much thunder during snowstorms and blizzards due to the muffling effect of the storms themselves.
Now, blizzards are basically intense snowstorms that can easily cause whiteout or snow blindness conditions. The National Weather Service (NWS) has much more specific criteria:

a winter storm that lasts for more than three hours and has sustained wind or frequent gusts of 35 miles per hour (MPH) or greater and considerable falling and/or blowing snow (i.e., reducing visibility frequently to less than ¼ mile).

As you can see from above, the main differences between thunderstorms and blizzards are (a) the occurrence of thunder and lightning, (b) the seasons in which they frequently occur, and (c) visibility conditions. In terms of similarities, both are specific weather phenomena that (1) typically operate within a blend of warm and cold conditions, (2) have the potential to generate thunder, and (3) have the potential to cause grievous harm and even death if appropriate shelter is unavailable.
https://w1.weather.gov/glossary/index.php?letter=b

https://www.livescience.com/32210-what-is-a-blizzard.html