One obvious similarity between Celia and the servant Adam is the love and loyalty they both feel. Celia loves Rosalind so much that she can't bear to be parted from her. As a result of her love, Celia tells her father to banish her as well when he decrees Rosalind to be banished from the dukedom. Due to her love for Rosalind, she very loyally travels with her into the Forest of Arden. Likewise, though just a servant of the late Sir Rowland de Boys' family, it's very clear that Adam loves Orlando very much. Adam loves Orlando so much that, despite how old Adam is, he also very loyally follows Orlando into the Forest of Arden when Orlando flees to escape his villainous brother.
We especially see Adam's love for Orlando in all of the things Adam says to praise Orlando's nature and character. For example, when Orlando returns to the house after having defeated Charles the wrestler, whom Orlando's brother Oliver had hoped would kill Orlando in the fight, Adam gives a speech proclaiming Orlando's praises, while also warning Orlando that Oliver has decided to burn Orlando's house to the ground in hopes of killing Orlando. We especially see Adam praising Orlando's character in the lines:
O, my gentle master!
O my sweet master! O your memory
Of old Sir Rowland! why, what make you here?
Why are you virtuous? why do people love you?
And wherefore are you gentle, strong and valiant? (II.iii.2-6)
In this passage, it is quite obvious that Adam is praising Orlando by calling him both "gentle" and "sweet." Beyond that, we even see that Adam is relating Orlando's character to the character of Orlando's late father, Adam's first master, as we see when Adam associates Orlando with the "memory of old Sir Rowland" (3). We also see Adam calling Orlando well loved, "virtuous," "strong," and "valiant."
Adam feels so strongly about Orlando, that when Orlando despairs at the news his brother is trying to kill him and says he has no place to turn to because he is penniless, Adam offers Orlando his life's savings, set aside for his retirement when he is too old to work. Not only does Adam generously give Orlando all of his money to rescue Orlando, he even offers himself as Orlando's faithful servant to accompany Orlando on his escape, despite how old Adam is. Adam's willingness to help Orlando, even his willingness to sacrifice himself for Orlando's sake, certainly shows not only how much he loves Orlando but also just how loyal he is to Orlando.