Declare War screen there are the two check box lists,
Enemy Allies and
Call Allies. I know what selecting the check boxes do, but what do the two possible colors represent? Sometimes the check boxes have a gold border, sometimes they are silver-blue border.
The checkbox indicates if an enemy should be co-belligerent. This means, they should be considered to have a military alliance and able to call their own allies in the war.
The box is grayed out when the co-belligerence is forced. For instance, attacking a vassal will always have their lord enter the war as an ally. Else, if it is not grayed out, you can chose the status yourself.
In general, if you chose not to have an enemy to be co-belligerent, then this enemy will not be able to call in their own allies, and taking provinces from them will cost twice the diplomatic power. The converse applies as well. Exception: In the case of forced co-belligerence, they are not able to call in their own allies.
Gold means you have the option of clicking it. This allows you to take their provinces for normal cost but allows them to call their allies as well. (Subject nations of any party will always enter no matter what)
Silver with a checked box means they are automatically called and co-billigerized. Such as the HRE Emperor defending Free cities or a vassal/PU member
Silver with an unchecked box means you most likely have a truce with them and can't pick them as a co-belligerent since you can't declare war on them but they can still answer defensive calls and have to pay the penalty if you take stuff from them.
A red X means they won't answer the call due to some reason (which can be seen by mousing over it). A green check means they will and why.
For allies you can offer them stuff to help you on offensive wars. These either cost favors, which are accrued from long-term relationships and answering each others calls, or giving them stuff in peace deals.
If the Icon is a red X but has a hand icon, it means that you don't have enough favors but the enemy has something they want and will help if you promise to give them at least some of the land they want in the peace deal, though you have to actually click the icon to switch it over offer-land icon, which will have a green check and you can then click the box, but make sure that you give them gains otherwise you take a massive trust penalty.