One piece of advice I used to hear a lot from my teachers was to write like you would speak. It is supposed to make writing easier and will put it in your own words. While this is a good piece of advice when writing for a blog or magazine, it is less than ideal when writing an academic paper or journal.
With personal writing, you can be a bit more lax about your choice of words. Depending on who it is for, the use of slang or abbreviations can be acceptable in personal writing. Think of personal writing as how you would write a Facebook post or an email to a friend. Very little structure is required, and you, as the writer, are free to do with it as you so choose. Your writing tone can be less formal. You are better off using more casual language - the kind you would use in every day conversations. What you are writing about may need to be understood by a wider audience.
With academic writing, there are rules that must be followed. Everything you write should have a structure to it and must convey your point in a direct way. Citation is one of the most important things when writing academically. While your work should be original, you have to support your argument through the use of facts and data. You and your work will have little credibility if you fail to include sources that back you up. The people reading an academic paper are there specifically to see your argument and to learn, so it's important to not waste their time with poorly supported statements.
When it comes to personal writing, remember that you are the audience. It is far more important that you enjoy reading what you have written than anyone else, so don't be afraid to use your own voice here. Personal writing allows you to be creative and original and can make for great mental exercise. Academic writings must be written so that your specific audience can enjoy it. You must remember to follow whichever formatting style is used in your field, whether it be MLA or Chicago style. In short, personal writing should be used for your own enjoyment, while academic writing is like a job.