My player made lvl 3 and chose Grave Domain sub-class for Cleric and so learned Spare The Dying as a Bonus Action - 30ft range. At lvl 1 He had already learned Spare the Dying cantrip as an Action -  touch range. 

He now has 2 variations of the same cantrip.

1. Can he cast this cantrip as a Bonus Action  or an Action on his turn?

2. Can he cast this cantrip as Bonus Action  AND an Action sequentially on his turn?

Cheers

Since it's a cantrip, you can do both, that's fine.

If you're using the 2024 rules, the number of spell slots you can expend on the same turn is only one: One Spell with a Spell Slot per Turn

On a turn, you can expend only one spell slot to cast a spell. This rule means you can’t, for example, cast a spell with a spell slot using the Magic action and another one using a Bonus Action on the same turn.

But a cantrip is cast without a spell slot.

Casting without Slots There are several ways to cast a spell without expending a spell slot:

Cantrips. A cantrip is cast without a spell slot. [...]

EDIT: also, there is SAC answer about this topic:

Can you cast a Reaction spell on your turn?
Yes, but you must abide by the rule of expending only one spell slot to cast a spell on your turn. For example, if you take a Magic action to cast Fireball using a spell slot and an enemy casts Counterspell, you can’t also then expend a spell slot to cast Counterspell targeting that enemy.