Logo Defined:

Main Entry: LOGO
Pronunciation: 'lO-(")gO also 'lä-
Function: noun
Inflected Form(s): plural log·os / -(")gOz /
1 : LOGOTYPE
Pronunciation: 'lo-g&-"tIp, 'lä-
Function: noun
a: a single piece of type or a single plate faced with a term (as the name of a newspaper or a trademark)
b: an identifying symbol (as for advertising)
2 : an identifying statement : MOTTO
Pronunciation: 'mä-(")tO
Function: noun
Inflected Form(s): plural mottoes also mottos
Etymology: Italian, from Late Latin muttum grunt, from Latin muttire to mutter
a: a sentence, phrase, or word inscribed on something as appropriate to or indicative of its character or use
b: a short expression of a guiding principle

Identity Defined:

Main Entry: IDENTITY
Pronunciation: I-'den-t&-tE, &-, -'de-n&-
Function: noun
Inflected Form(s): plural -ties
Etymology: Middle French identité, from Late Latin identitat-, identitas, probably from Latin identidem repeatedly, contraction of idem et idem, literally, same and same
1 a : sameness of essential or generic character in different instances b : sameness in all that constitutes the objective reality of a thing : ONENESS
2 a : the distinguishing character or personality of an individual : INDIVIDUALITY
b : the relation established by psychological identification
3 : the condition of being the same with something described or asserted <establish the identity of stolen goods>

*Above definitions found in the Merriam-Webster Dictionary Online