Term for different types of race: racing by turns and racing together

Question

Competitive racing (whether running, biking, skiing, or whatever) is usually carried out in one of two ways:

1. Two or more competitors start at the same time and race side-by-side; the first to cross the finish line is the winner.

2. Each competitor starts alone, with no other competitors in sight; each run is timed (or otherwise measured), and the person with the fastest time (or otherwise best score) when all competitors have completed their turn is the winner.

Category 1 normally includes disciplines like track, sprint, bike races, swimming, cross-country skiing, etc. Category 2 tends to include disciplines like downhill skiing and bobsled. Sports like javelin, ski jumping, high and long jump, etc., are done in the same manner, though time is not the standard measured there.

Do these two basic types of carrying out competitive racing have individual names? For example:

The slalom race was organised as a _____ event, while cross country was a _____ event.

Answer 1

For your category 2 I would suggest time trial:

a race in which competitors are timed individually on a set distance over a course or track, especially to qualify for a successive event.

^{dictionary.com}

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I don't know of any specific name for your category 1. The vast majority of races are with all competitors competing at the same time. When they're not, I would expect it to be explicitly detailed (i.e. by calling it a time trial). So race on its own without further context would normally suffice. But of course your example sentence needs something explicit rather than implicit.

Collins dictionary offers wording to explain the opposite to time trial:

In cycling and some other sports, a time trial is a contest in which competitors race along a course individually, in as fast a time as possible, instead of racing directly against each other.

^{(emphasis mine)}

However, this doesn't offer an easily recognisable noun/title like "time trial".

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The wikipedia article on time trial suggests that the other type is called mass start, although the article on mass start seems more relevant to e.g. marathons with hundreds of competitors and not to e.g. track racing where each of 8 competitors has their own lane.

Happily, though, cross country is akin to marathons in the large number of competitors without specific lanes, so mass start will work in your example sentence:

The slalom race was organised as a time trial event, while cross country was a mass start event.

Answer 2

A race wherein participants race against each other simultaneously is a "race." I'm not aware of a single word for "racing [individually] against the clock."