Final answer:
Software distributed for free with a suggested payment if you continue to use it is called Shareware. It differs from Freeware, Open-source, and Trialware, which have different usage and distribution terms.
Step-by-step explanation:
Software that is distributed for free, but often with the condition that you pay for it if you like and intend to use it, is called Shareware. Shareware is a marketing method for software where the software is distributed without initial payment, but encourages users to pay a fee if they find the program useful and continue to use it. This is different from Freeware, which is completely free without the expectation of payment, and Open-source software, where the source code is available for users to modify and distribute. Trialware, on the other hand, is software that is distributed for free for a limited period of time, after which the user must pay to continue using it.