If I have more than one type of unit in my force, say two Battle Grenadiers for instance, do I need to play a specific card per unit or move whatever unit would give me the best advantage for firing, getting to cover etc?

Not sure I understand the question. You have two Battle Grenadiers in your army, ok. You should then certainly have one card for each unit, and you should be able to tell which card relates to which unit. When it's your turn, you activate whichever unit you want.

My question is really asking if out of the two identical cards, do they relate to a specific unit or could I activate either unit, assuming that neither had activated.

This came up when I played AT-43 and the answer there was use any unit that matched the card.

If it is the case that a specific card belongs to a single, specific unit, how do people mark the card or unit so they know which one belongs to the other?

Imagine you have two Ludwigs, one of them takes 3 hits, and you mark that on one of your cards. The other Ludwig remains unharmed, but than that first one takes another 2 hits, where are you going to mark that? Of course you have to mark that same card, destroying that walker, instead of adding two hits to the other, unscathed card.

If you have more than one unit of the same type you need to keep track of what card relates to which unit (which is just one reason why I never use multiples). Some people add a dot of a specific color to the card, and paint that same color around the base of the unit.

I put bumper number on all my vehicles and pace a dice on the base to count the damage.

Londoncopper said:

The two games are basically the same. In at43 you could use any card for any unit but you still had to record that units damage/activation. Otherwise the game would not play correctly. AT43 had white boxes on the cards to record where you wanted the damage to go but that was all you could control.