The number one thing you need to consider when working two jobs in the same field is conflict of interest. The ultimate answer to your question is: if you don't know whether there is a conflict of interest, you need to ask your manager at both employers. Now, for the juicy bits!
To determine for yourself if your dual employment represents a conflict of interest, ask yourself the following questions:
- What software will I be working on with the two different companies? If the software has the same or very similar feature sets, then you have a definite conflict of interest, since you know what each company is doing, and can tell the other employer at any point.
- Do the two companies that I'm working for consider each other to be competitors? If the companies see each other as competitors, you definitely have a conflict of interest, even if the different employers have you working on completely different projects. If you aren't sure if the companies are competing against each other, look at each company's mission statement, if it's available. You should be able to find this on the company's public facing website in their "About Us" section.
- What unique skills did I have that caused each of the companies to hire me? Holding an undergraduate degree in computer science is not a unique skill. Holding a higher degree, while possibly more rare, also isn't a unique skill. However, if both companies hired you because you excelled in courses related to Computer Graphics (as an example), then that would be a unique skill, and could possibly be a conflict of interest, even if the two above points are not.
Another important concept that people sometimes can't "get on board with" regarding conflict of interest is the accusatory nature of it. "I'm a good person. I would never..." Understand that conflict of interest isn't about you, and whether you would do it, but more that you could do it, and to prevent that from happening, you could end up losing both positions. Not only could you lose both positions, but you also risk civil complaints and legal action.
Finally, and this is a bit on a bird walk from the original question, but it's tangential and you may want to know: You must also consider conflict of interest while working on your own, personal projects. If you are working on something that would improve upon the some task that your current employer is doing, and you further have even a fantasy about commercializing your project, then you have an extreme conflict of interest, and you need to inform your employer about your project, or stop working on it.
Software Development in the current era is at the crux of almost everything. "Ubiquitous" is an underwhelming description, honestly. As software developers, engineers, or other "STEAM" field employees, we need to take extreme caution with conflict of interest, because the average person isn't going to be merciful if our employers determine that a conflict exists.
Good luck and Godspeed!