確かにトレーニングは英語で training と言いますが、筋トレやジョギングは運動の一種なので言い換えられます。
運動 - exercise, workout
workout - 運動、トレーニング
私は2回のトレーニングをします - I'm going to work out 2 times (today). First, I'm going to lift some weights/do some squats... and then I'm going to go jogging もしくは I'm going to exercise two times (today). First, I'm going to do some pushups/lift some weights and then I'm going for a jog.
I'm going to do two different workouts. First, I'm going to focus on building muscle then I'm going to do cardio/ then I'm going to go jogging もいい気がします.
ジムの話の場合はcardio workout はだいたい running, skipping, elliptical machine など
cardio - cardiovascular - 心臓や血管のことを指します。
過去だったら
I worked out twice today. First, I worked on my chest then I went jogging もしくは I exercised twice today. First, I worked on my legs and back then I went for a jog.
筋トレ - (直訳) muscle training. Muscle training はやや不自然だと思います。具体的にどんな筋トレ(腕立て伏せ、スクワット, lift weights - ダンベルとか)もしくは体のどこをトレーニングするを言うのが自然だと思います。I'm gonna do muscle training とか I did muscle training はネイティブから聞きません. I did some weight-lifting today とか Today was a leg day とか I worked on my chest today/ I did a full body workout などの方が自然だと思います。
work out -動詞
workout - 名詞