Well pretty much they've been copying each other ever since the 1980s. For example, most of Microsoft's older tools (fdisk, etc.) were originally IBM's tools but were given rights to Microsoft after they left IBM to become standalone. MS-DOS for example was thought to be a heavy edit of 86-DOS created by Gary Kildall, an IBM employee. Older Windows users remember MS-DOS as the underlying 16-bit OS which would allow entry into 32-bit mode.
Apple has technically been seperate from Microsoft if you look at some of what they used. And they're quite infamous as most of their systems used unique hardware (with the exception of System 6-7 which used the Motorola 68k) but the primary battle began when both companies were compared in terms of different fields, such as performance, reliability, customer support, etc.
In the modern day most of the code can be intertwined to create multi-platform support. This supposedly eliminated some of the battles outside personal opinions.
If this is about Microsoft supplying tablets for the Windows 8 operating system, and the Windows Phone operating system, then yes in my opinion they are copying Apple. But this is common in marketing as most competitors will compete with a company they've been rivaling by creating something "better". Compact stuff was idealized by Apple but it wasn't technically restricted to them, so I wouldn't say they're "copying" but rather building upon an idea passively.