してます vs します
what is the difference?
してます is a conversational casual contraction of しています. In the same way している can become してる. する and している are not necessarily casual, they are simple neutral (dictionary) forms, less polite than the します and しています forms, but not 'casual' in and of themselves.
You can use the contracted forms in casual conversation, blogs, letters to friends, etc. You should not use them in formal writing.
The ～ている form indicates a currently ongoing activity. The ～する form indicates an activity that is done or can be done in general or an activity that will be done in the future.
- する = します (To do) 「テニスをします。」'I play tennis.' [Simple statement]
*している = しています (To be doing) 「テニスをしています。」 'I am playing tennis.' [Currently ongoing activity]
The use of ～ている does not necessarily mean that at this exact moment the activity is happening, more that it is being done regularly in the current time frame (enrolled in a tennis club as opposed to just being able to play tennis).
If, for example, you have recovered from an illness that didn't allow you to attend school for a long time and someone were to ask you whether or not you are attending school you would respond 「今はがっこうに行っています.」'I am going to school now.' On the other hand, if someone wants to know whether you attend school or if you are home-schooled, you would respond 「がっこうに行きます」'I go to school'. (Simple statement)
The difference between the simple forms and the progressive forms will require further study, especially as they apply to past and future tense usages.
Like everyone has said already, "します" expresses an action that will happen for suru-verbs like 擁する (yousuru, will possess/to possess) in a more formal way than just "する" by itself. "してます" expresses an ongoing action for suru-verbs. It can also be written as "しています", which doesn't really make a difference (but sounds a little more casual). "擁する" would become "擁してます" (youshitemasu, is/are possessing). Its less formal counterparts are "してる" or "している".
You said that しています sounds more casual than してます, while the opposite is true.
While not used much very often contemporarily, 擁する has a few other meanings: hug; embrace; protect; lead. There should, however, be no need to include this verb, as it is either too obscure or too advanced (depending on your perspective) for the current audience.