The verb ta form is used as the past affirmative form in casual speech. But this form, grammatically, indicates a completion of an action.
e.g. watashi ha rinngo wo tabeta(/tabemashita). I ate apple.
ie ni kaetta(/kaerimashita). I returned home.
Here, what you listed is plain form and masu form of v-ta. Take "tabeta" for example.
Ordinary verb: taberu. 食べる
ta form: tabeta 食べた（plain form）/ tabemashita 食べました（masu form）
If you are not sure when to use "Tabeta" and "Tabemashita", then, this question will be when to use "verb's plain form" and "verb's masu form".
Masu form is more polite and formal than plain form, so when you talk to strangers, teachers, person who are older than you, and so on, it would be better to use masu form.
Since sentences that end with the plain form are less formal, so you can use plain form when talk to close friends, the person younger than you. Besides, when you write a report or essay, it would be better to use plain form as well.
For more information: https://www.coscom.co.jp/japaneseverb/japaneseverb01-jpr.html
Hope this would help:)