Yes, just "phone number" can refer to a cell phone number. When you ask someone for their "phone number" usually it is a home or cell phone number. If you want to be specific, ask for their "cell phone number"

Hello Helen, I hope I understand your question. When asking for a telephone number most people will give their cell phone numbers, or indicate that the number they are providing is a business number (office) or a home phone (land line). A good way to ask is "What number is the best number to reach you?" and then the person may respond "My cell" or my "business" or when a person gives you a telephone number it is not impolite to ask "Is this your cell number? or "What is the best time to reach you?" I always ask if the person "accepts texts" because I do not want to assume that everyone who has a cell phone has an unlimited data plan. I hope this helps. Skye