Japanese katte v. motte?

Question:

I'm taking Rosetta Stone Japanese and it doesn't translate anything. Usually this is OK, but I'm really stumped on this one. Here are two sentences:

kare wa kuruma o motte imasu. (Picture of a man with his hand on a car behind him)
onnanokotachi wa uma o katte imasu. (Pic of two girls hugging a horse. On girl is in front of it, the other on it)

Whenever I come across motte or katte, their meanings seem inconsistent. Do they mean "have," "with," "behind," "touch?" I can't figure it out or what the difference is.

Answer:

kare wa kuruma o motte imasu.
--> He has/owns/possesses a/the/this car.

onnanokotachi wa uma o katte imasu.
--> These girls have/keep/own a/the/this horse. ("kau" is used for animals/pets)

if you want to say "girls patting a horse";
--> "uma o sawatte iru shoujo-tachi (onna-no-ko-tachi)"