colloquially no.

but start = to commence proceeding etc. that's why we have a starting time at sports competitions and for events and departure times when a journey will start.

"the competition will start at 17:30 next Wednesday"

Begin = the first part of to do something.

"The match will begin at 17: 30 and end at 19:00 next Wednesday.

competition = a series of individual games or matches.

match/game = one of many individual games/ matches during a competition.

so there is considerable overlap, and now i believe they are used interchangeable although there is a very small subtle dictionary definition to argue about.

we start engines you have to set a process in motion.

we start or sometimes begin arguments

we start or begin adventures/journeys

we start a horse race by dropping a flag usually

we start processions informal or formal processions

we start but I think most often begin ceremonies "THE CEREMONY GOES THROUGH STAGES"

we start to write a book but some may say begin to write a book.

In the UK starting Engines and Horse races has become the set phrase to use.

it may be different elsewhere. For other times I think you can use either,