Is there any physical appearance difference between a wizard's familiar, from find familiar, and the animal it is copying?
It is a Spirit, but it copies a beast so it looks like a beast.
No, its appearance physically is the exact same as the animal (unless a spell says otherwise, it does what it says it does). In this instance the spirit is copying a beast. It makes no mention of any halos or horns or glitter that would let others know it's not a beast. It will however be detected as a fey, fiend, or celestial if your paladin uses Divine Sense or if someone casts the detect evil and good spell.
It's up to you and your DM. (to some extent)
As always, a spell does what it says it does (emphasis mine):
You gain the service of a familiar, a spirit that takes an animal form you choose: bat, cat, crab, frog (toad), hawk, lizard, octopus, owl, poisonous snake, fish (quipper), rat, raven, sea horse, spider, or weasel. Appearing in an unoccupied space within range, the familiar has the statistics of the chosen form, though it is a celestial, fey, or fiend (your choice) instead of a beast.
The spell does not mention the appearance of your familiar, only that the form matches a certain beast. While the type of your familiar will be one of celestial, fey or fiend, that will not affect its appearance.
This gives you some freedom on your familiar's appearance. By that I mean the actual color, the species, having a spot of different color so it's recognizable by your friends or the exact opposite: having a generic beast looking familiar that will be indistinguishable from any other one in the wild by appearance. The DM can rule that your character has no power over this and make the decision himself about what the beasts looks like.
Keep in mind that this will not change the statistics or game features of your familiar as noted by the spell:
[...]the familiar has the statistics of the chosen form.
This is 100% a flavor decision, and depends on how your DM wants it to work. I would say that since (a) the familiar obeys its master, and (b) the spirit "takes an animal form", that means the spirit should be able to make cosmetic choices about the specific form it takes.
Those choices probably need to be within the normal range of the animal form, i.e. no green cats or furry owls, but the specific species, color, markings, size, etc. ought to be freely chosen within normal parameters. For example, there are owl species as small as a couple of ounces, to as big as 5 pounds, so anything within that range is probably fine.
Remember that whatever form it picks, it appears as exactly that same form every time it appears, unless and until you actually re-cast the spell to allow it to change its form.