応援 and 声援: support and audible cheering
Distinguish broad support from encouragement delivered by voice.
Supporting and helping
応援, read おうえん, means support or encouragement. 友人のチームを応援しました。 means supporting a friend's team.
仕事が忙しいので、応援を頼みました。 says that help was requested because work was busy. 応援 is not limited to cheering from the stands.
Encouragement by voice
声援, read せいえん, means vocal encouragement. 選手に声援を送りました。 means cheering for the athletes.
観客の声援が聞こえました。 says that the spectators' cheers were audible. Do not make the athletes the people cheering.
Forms of support
遠くから応援しています。 means supporting someone from afar. It does not necessarily establish shouting aloud.
声援は聞こえましたが、観客の顔は見えませんでした。 says that cheers were heard but spectators' faces were not visible. Separate auditory and visual scope.
Does 仕事の応援を頼みました necessarily concern cheering at a game?
Show the answer and why
No. It concerns requesting help with work.